PAP Algebra 2. Unit 4B. Quadratics (Part 2) Name Period
|
|
- Shonda Melton
- 5 years ago
- Views:
Transcription
1 PAP Algebra Unit 4B Quadratics (Part ) Name Period 1
2
3 After Test WS: 4.6 Solve by Factoring PAP Algebra Name Factor. 1. x + 6x x 8x x + 7x x 3x x + 7x x + 10x x 11x x 10x x + 17x 6 Solve by factoring x 1x 3 = x 11x 3 + = 13. = 5 x 15 x 3
4 14. 40x 1x 63 + = x x x = x = 5x x 15x 6x 0 + = 18. 6x 8x 16 + = 19. = + 5 x 6 x 4
5 Solving Quadratics by Factoring Worksheet 4.6 Name Per Solve by factoring. 1. x + 5x + 6 = 0. x x 1 = 0 3. a a = 0 4. t + t 19 = 5 5. x + 15x + 30 = 6 6. d d + 10 = = 0 x x = 15 a a 9. c c = = 0 x x 11. h 7 = t 15t + 6 = d + 10d + 18 = = 3 x a 3a + 17 = = 0 n n = + 3 x x x 18. 6t 15t 36 = 0 Find the dimensions of the rectangles below x +7 x +8 x 50 in x+3 34 ft 5 Page 1 of
6 Write a quadratic equation to represent each situation. Solve by factoring. 1. Thirty-five less than the square of a number is the same as times the number. Find the number.. Find two consecutive positive integers whose product is Find two consecutive odd integers such that the square of the first, added to 3 times the second, is Find three consecutive integers such that the square of the first, increased by the last, is Find three consecutive integers such that the product of the first and third exceeds the product of 8 and the second by Ms. Powers can kick a soccer ball up into the air with an initial velocity of 44 feet per second. Using the formula h = vt 16t, where h = height above the ground, v = initial velocity, and t = time in seconds, find how many seconds it will take for the ball to return to the ground. 7. Suppose you transform a square by increasing one side by 4 units and decreasing the other side by units. If the area of the resulting rectangle equals 16, how many units long was the side of the original square? 8. Suppose you transform a square by increasing one side by 1 units and decreasing the other side by 8 units. If the area of the resulting rectangle equals 44 how many units long was the side of the original square? 9. The length of a rectangle is 4 more than the width. Find the width of the rectangle if the area is The length of a rectangle is 5 times the width. If the length and width are both increased by, the new area would be 85. What is the original area? 6 Page of
7 PAP Algebra II 4.6B Notes GCF greatest common factor EX1) 6xy 9x + 3y EX) a b 10ab 3 EX3) r m 8r m + 1r m EX4) 3z + 4y 4 3 Difference of Squares a b = ( a b)( a + b) EX 5) x 81 EX 6) y + 49 EX 7) 4x 5 EX8) 9a 49b EX9) 16m r EX10) c x 3 3 Sum/Difference of Cubes a b a b a ab b = ( + )( + ) a b = ( a b)( a + ab + b ) EX 5) 3 x 7 EX 6) 3 y + 64 EX 7) 3 8x 1 EX8) 16c x EX9) 3 6 8m r EX10) 6 3 7a 15b 3 3 Factor by Grouping EX 11) 3 x x x EX1 ) 3 6x 3x 4x + 7
8 COMBINED. EX 14) d d + d EX 15) 3 6y 8y + 8y EX 16) g 3 5g EX 17) + 3 4c 500 EX 18) 4 5a 0a EX 19) 3 v v v Ex 0) Find three consecutive integers such that the product of the first and the third is 35 greater than the product of the second and 5. EX 1) Find four consecutive even integers such that the product of the second and fourth is 16 less than the product of -3 and the sum of the first and third. 8
9 PAP Algebra II WS 4.6B Name: Factor the following completely. If it does not factor state not factorable. 1) 4x 1x ) x 0x + 1x 3) m + 7z 4) 3 x x x ) 3 9x 16 x 6) m 11m + 1 7) 3 f f f ) 9 p q 5q 7 9) 3 8x 15 10) 3 0n + 4n 5n 1 9
10 11) Find two consecutive odd integers such that the square of the larger diminished by three times the smaller equals 34. 1) One number is 10 less than 8 times another number. If their product is -3, find the numbers. 13) If the sides of a square garden are increased by 4 meters, the area of the new larger square garden is 56 square meters more than the area of the original smaller garden. How long was the side of the original smaller garden? 14) One leg of a right triangle is 3 cm shorter than the other leg. If the hypotenuse is 15 cm, what is the length of the longer leg? 15) A path of uniform width is constructed around a 0 X 5 meter rectangular garden. If 196 square meters of brick are used to construct the path, what is the width of the path? 10
11 PAP Algebra II Notes 4.7 Complex Roots, Solve by Graphing, Solve by Quadratic Formula Complex numbers 3 + 4i 10i 11 Irrational Numbers Real Numbers e π 3 7 can not be written as a fraction 1 8 Rational Numbers can be written as a fraction. 5. e π 11 7 Integers Today we are going to work with some imaginary (i.e. complex) numbers! The base for an imaginary number is i, which is the square root of negative 1. i = 1 This is imaginary because it does not exist. Put 1 what does it say? Complex numbers have a real part, and an imaginary part. a and b is the imaginary part. in your calculator and EX1) Identify the real and imaginary part of these complex numbers: a) 3+ i real: imaginary: b) 7 9i real: imaginary: c) 5i 3 real: imaginary: d) 4i real: imaginary: e) 8 real: imaginary: + bi is the form of a complex number. a is the real part, This applies to quadratics because sometimes we will have roots that are not real. 11
12 An equation of the form ax + bx + c = 0 can be solved by using the quadratic formula: x = Use this formula to solve each of the following. Remember to set equal to zero first! 1. 8x x - 1 = 0. x + 3x - 1 = 0 b ± b 4ac a 3. x x + 1 = 0 4. x 4x + 13 = x + 4x = x +7x - 4 = x +3 In the quadratic formula, the expression b 4ac is called the discriminant. We can use this to determine how many solutions an equation has and if they are real or imaginary. Value of discriminant b 4ac>0 b 4ac=0 b 4ac<0 Number and type of solutions Example Graph Find the discriminant of the following equations and give the number and type of solutions of the equation. Remember to set equal to zero! 1. 7x x + 5 = 0. 3 x + 1x + 1 = x 5x + 1 = 6 7x 1
13 PAP Algebra II WS 4.7 Name: Use the quadratic formula to find the roots for the following quadratics. Tell whether the roots are real or imaginary. Put all complex roots in the form a+bi. 1) y x x = ) y = x 5x 3 3) y = x x 3 Roots: Roots: Roots: real imaginary real imaginary real imaginary 4) y x x = ) y x x = 5 7 6) y x x = + 7 Roots: Roots: Roots: real imaginary real imaginary real imaginary Find the value of the discriminant. Describe the number and type of roots: 7) y x x = ) y x x = 4 5 9) y = x x
14 10) A quadratic equation has real rational roots. Which of the following could be the value of its discriminant? a. -10 b. 10 c. 5 d. 37 1) Factor: 3 8m 7 13) Solve by factoring: 16x 5 = 0 Tell what intervals the following quadratics are increasing or decreasing. 14) y = x 7x + 5 inc: dec: 15) y = 3x 11x 4 inc: dec: 16) What is the b value for the quadratic y = 3x + bx 1 if the roots are x=1 and x=-4? 14
15 Pre-AP Algebra 4.8 Write Quadratic Equations Name: Ex 1) Write an equation for the parabola with the following roots in standard form. Graph your answer to verify. a) x = 3 and x = -8 b) x = only c) x = 3i and x = -3i d) x = 4+i and x = 4 i e) x = 3+i and x = 3 i f) 1 x =, x = 3 15
16 INCREASING: From left to right the graph is going up. DECREASING: From left to right the graph is going down. Ex ) Write the intervals where f(x) is increasing and decreasing. g) y = x 9x + 1 inc: dec: h) y = x + 7x 4 inc: dec: Ex 3) Find the value of b in the equation y = 4x + bx 1 if the function has roots of x = and = 6 1 x. Ex 4) Over what interval(s) is the parabola in Ex 3 positive? 16
17 PAP Algebra II 4.8P Quadratics Practice Name: 1. Graph the function. y = -3(x +1) +4 Domain: Range: Axis of Symmetry:. Given the factored form of the equation: y = -4(x -5) (x +3) a) identify the root/s b) convert to standard form c) identify the y-intercept 3. Consider the graphs of the following equations. List the equations in order from narrowest graph to widest graph. a) y = -4x b) y = 1 3 x c) y = 5 3 x d) y = -x b= 4. Find the value of b in the equation y = x + bx 3 if the vertex is (3,-1). 5. Write the equation for this parabola in a) vertex form: b) factored form: c) standard form: 17
18 6. Write equation for the path of the golf ball in: a) vertex form: b) factored form: c) standard form: 7. A rocket is shot straight up into the air from the top of a 30 foot cliff with an initial velocity of 3 ft / sec. The equation for the path of the rocket is a) What was the maximum height of the rocket? b) When did the rocket reach it s maximum height? c) When did the rocket land on the ground? d) How long after it was shot did it land on the ground? e) What is a realistic domain for this situation? h t t = Graph the following quadratic inequalities. Be sure to label at least 3 points. a) y 1 < 3( x 5) + 4 b) y ( ) 4 x 3 18
19 9. Find the vertex of the following parabolas. V= a) y = x + 6x 9 V= b) y = 3x + 4x A football is kicked from the ground at the 10 yard line, and it lands on the 50 yard line. If the maximum height of the football is 80 yards, what is the equation for the path of the football? F(x)= V(x)= S(x)= 11. Find all roots of the following parabolas. Simplify completely! Put all complex roots in the form a+bi. a) y = 3x + x b) y = 4x + x 3 Roots: Roots: 1. Write the equation in standard form for the parabola with roots: a) x= -9 only b) x = ± 7i c) x = ± 5i 19
20 13. Find the best fit quadratic equation to fit through the following data points. (round to 3 decimal places) TIME(s) HEIGHT(m) a) Best fit quadratic: b) What is the maximum height of the object? c) When does the object hit the ground? 14. A golf ball is hit from the top of a hill that is 16 feet high. It reaches it s maximum height of 87 feet 9 seconds after it was hit. a) What is the equation for the path of the golf ball? (round to 3 decimals) V(x)= S(x)= b) When does the golf ball hit the ground? 15. Use interval notation to identify what intervals the parabola y = 3x 4x + 5 is increasing and decreasing. Increasing: Decreasing: 16. Factor the following quadratics completely and find the roots: a) y = x 16 factored: roots: b) y x x = factored: roots: c) y x x = factored: roots: 0
21 d) y x x = factored: roots: e) y x x = factored: roots: f) y x x = factored: roots: 17. Write the equation and graph the area of the set of all right triangles whose base is three more units than the height. Area = What is a reasonable domain and range for this situation? Domain: Range: 18. Determine whether each equation has no solution, one real solution, two real solutions or two complex solutions. I. 0 = x + 5x + 1 a) no solution b) one real solution c) two real solutions d) two complex solutions II. 0 = x + 6x + 9 a) no solution b) one real solution c) two real solutions d) two complex solutions III. 0 = x + 3x + 5 a) no solution b) one real solution c) two real solutions d) two complex solutions 19. Fill in the table for g(x) given that g( x) = f ( x 3) + 3. x f(x) x g(x)
22 Pre-AP Algebra WS 4.8 Writing Quadratics Equations Name: 1. Write the equation of a quadratic with solutions at -3 and 15.. Write the equation of a quadratic with an a value of 3 and solutions at -3 and Write a quadratic equation of the form ax bx c + + = 0that has roots 8 and Write the equation of a quadratic given the following graph. 5. A rectangular enclosure at a zoo is 35 feet long by 18 feet wide. The zoo wants to double the area of the enclosure by adding the same distance, x, to the length and the width. Write and solve an equation to find the value of x. What are the new dimensions of the enclosure? 6. Write the equation of the quadratic with solutions at 3± 6i. 7. Write the equation of the quadratic with solutions at 4 ± 4i. 8. Write the equation of a quadratic whose discriminant is -16 with an a value of 1 and a b value of -18.
23 9. Write the equation of the quadratic in the graph shown. 10. Find two consecutive odd integers whose product is 79 greater than their sum. 11. The length of a rectangular picture frame is 6 inches less than twice the width. Find the width of the frame if the area of the picture frame is 80 square inches. 1. Suppose you transform a square corn field by increasing one side by units and decreasing the other side by 3 units. If the area of the resulting corn field equals 4, what was the length of the original corn field? 13. A rectangle is 5 inches wide and 1 inches long. How much should be added to the width of the rectangle to increase the diagonal by 7 inches? 14. Find three consecutive even integers such that the product of the first and third exceeds the product of the second and 8 by 16. 3
24 4
25 Pre-AP Algebra Notes 4.9 Solve and Graph Quadratic Inequalities Name: 1. a. Given ( ) y x + 1 4, what are the transformations being applied? b. Would you use a solid or dotted line to graph? c. Sketch the parabola on the graph to the right. b. Using the inequality y ( x + 1) 4, test the following ordered pairs to determine where shading of the solution set should occur. ( 3,0) ( 1, 1) (3, ) c. What ordered pair is usually an excellent test point? Why? When would this point not work to check for the solution region?. a. Given y x x + 1, where are the roots? The vertex? b. Would you use a solid or dotted line to graph? Why? c. Sketch the parabola on the graph to the right. d. Using the inequality y x + x 1, test the following ordered pairs to determine where shading of the solution set should occur. (0, 15) (0,0) (,0) Sketching the Graph of a Quadratic Inequality: 1) Sketch the graph of the parabola y = ax + bx + c. Use a solid line for and a dashed line for > <. ) Test one point inside the U-shaped and one outside. 3) Only one of the test points will be the solution. Shade that region. Ex. 1: Sketch the solution for y 3x 6x 5
26 Ex. : Sketch the solution for y -x + x + 4 Word Problems: 1. The path of a football kicked from the ground can be modeled by h =.0x + 1. x where h is the height (in yards) and x is the horizontal distance (in yards) from where the ball is kicked. The crossbar on a field goal post is 10 feet above the ground. a. Write an inequality to find the values of x where the ball is high enough to go over the crossbar. b. Solve the inequality. c. A player attempts to kick a field goal from 5 yards away. Will the ball have enough height to go over the crossbar from this distance?. The arch of the Sydney Harbor Bridge in Sydney, Australia, can be modeled by y =.0011x x where x is the distance in meters from the left pylons and y is the height in meter of the arch above the water. If the road is 5 meters above the water, for what distances x is the arch above the road? 6
27 Pre-AP Algebra WS 4.9 Solve and Graph Quadratic Inequalities Name: Using your graphing calculator, plot at least three accurate points to form the boundary line. Shade the correct region and then list ordered pairs that could be solutions. 1. y ( x ) + 3 y > 3( x + 1) + 6 y y x x 3.Which of the points given would satisfy the inequality? There can be more than one answer. y x + x 1 a. (1, 3) b. (, 0) c. (5, -) d. (-, 4) Application Problems 4) You decide to start at the left base of a mountain and show off your hiking skills. The mountain might be represented by the function y = -.006(x 310) You need to use oxygen above 00 feet. You are asked to analyze the part of the path that is safe to hike without oxygen? a. Write the inequality b. Solve for reasonable solutions. c. Identify the vertex of the mountain d. Describe the window used on your graphing calculator. X min= X max= Y min= Y max= 5) The Arc-de-Triomphe in Paris might use the equation y = -.444x x +.1, to make the arch at the top. A row of decorative stone is 85 feet above the ground. Painters need you to analyze the area above the stone so they can paint that area. a. Write the inequality b. Solve for reasonable solutions. c. Identify the vertex of the arch 7
28 6) The Eiffel tower in Paris has four arches at the base. Each one has an equation similar to y = -.0x + 3x.5. If they are starting at the right and left bases and painting up the arch, what domain will get painted if the need to stay under 65 feet? a. Write the inequality b. Write the domain of the arch that gets painted on both sides? 7) The Grand Canyon has valleys shaped like parabolas. The inequality y.006x represents the part of a canyon that can be seen from an observation tower. 10.8x 400 a. Find a good fit window. b. Write the domain of the valley that is below sea level? (allowing negative values) c. Explain how you decided on a good fit window. 8) A plane is flying over the Grand Canyon. It follows the function f(x) = -.5(x 1000) , where x is minutes and f(x) is height in feet. For what times, x, is the plane above 0,000 feet? a. Write the inequality b. Write the times of the plane? 9) A picture is 1 inches by 14 inches. You are going to add a frame that is x inches thick. You want the resulting framed picture to have an area less than or equal to 500 square inches. What is a reasonable solution for the thickness of the frame? (Assume the frame must be at least 1 inch thick) a. Write the inequality b. What is a reasonable solution? 10) Twenty-eight less than the square of some number is 3 times the same number. Find the number. Is there more than one possibility? 8
29 Name: Solving Linear Quadratic Systems Algebraically Algebra 1 Date: In this lesson we will begin to work with solving linear-quadratic systems of equations. Recall that to x, y that satisfy all equations in the system. We solve a system we must find the set of all points ( ) will review this concept with an example from linear systems. Exercise #1: Consider the linear system shown to the right. y = x + 5 x + y = 15 (a) Solve this system algebraically using the substitution method. (b) Explain, in graphical terms, what the ordered pair from (a) represents. The substitution method was used above because it is the only method that we can use to solve linear quadratic systems algebraically. Solving such systems requires solving a quadratic equation. Since we are working with quadratics, it is natural to expect more than one answer. This has a graphical connection as Exercise # will illustrate. Exercise #: Consider the sketch of a line and a parabola shown at the right. (a) What is the maximum number of intersection points that a line and a parabola could have? Illustrate with a picture. (b) What is the minimum number of intersection points that a line and a parabola could have? Illustrate with a picture. (c) Is it possible for a line and a parabola to intersect in only one point? If so, illustrate with a picture. Algebra 1, Unit #6 Quadratic Algebra L16 The Arlington Algebra Project, LaGrangeville, NY
30 Exercise #3: Solve each of the following systems of equations algebraically and check using STORE on your calculator. In each case the substitution method should be used to begin the process. (a) y = x + 4x 1 y = 7x + 9 (b) y = x + x + 7 y = 6x + 3 (c) y = x + x 6 3x + y = 1 (d) y 10x = 5 y = x + 7x + 5 Algebra 1, Unit #6 Quadratic Algebra L16 The Arlington Algebra Project, LaGrangeville, NY
31 Name: Skills Solving Linear Quadratic Systems Algebraically Algebra 1 Homework Date: 1. Which of the following is a solution to the system of equations shown to the right? (1) ( 4, 7 ) (3) ( 3, 0 ) y = x 9 y = x + 3 () ( 4, 1) (4) (, 5 ). Mateo produced the following table on his calculator to find the solutions to a linear-quadratic system of equations. Based on this table, which of the following sets gives the x-values that solve this system? (1) { 4, } (3) {3, 6} () { 4, 3} (4) {,1} 3. Which of the following is not a possible number of solutions to a linear-quadratic system? (1) 1 (3) 3 () (4) 0 Solve each of the following linear quadratic systems of equations algebraically and check using STORE on your calculator. 4. y = x + 5x y = x 5. y = x 3x + 3 y 3x = 6 Algebra 1, Unit #6 Quadratic Algebra L16 The Arlington Algebra Project, LaGrangeville, NY
32 6. y = x + x 8 4x y = 5 7. x y = 10 y = x x Applications 8. The price C, in dollars per share, of a high-tech stock has fluctuated over a twelve-year period according to the equation C = x x, where x is in years. The price C, in dollars per share, of a second high-tech stock has shown a steady increase during the same time period according to the relationship C = x (a) For what values are the two stock prices the same? (Only an algebraic solution will be accepted.) (b) Determine the values of x for which the quadratic stock price is greater than the linear stock price. State your answer as an inequality. (Hint: You should be able to answer this almost immediately based upon your analysis in part (a) above.) Reasoning 9. Which value below for b would result in the linear-quadratic system y = x + 3x + 1 and y = x b having only one intersection point? Justify your answer algebraically, graphically or with a table. (1) 1 () (3) 3 (4) 4 Algebra 1, Unit #6 Quadratic Algebra L16 The Arlington Algebra Project, LaGrangeville, NY
Solving Linear Quadratic Systems Algebraically Algebra 1
Name: Solving Linear Quadratic Systems Algebraically Algebra 1 Date: In this lesson we will begin to work with solving linear-quadratic systems of equations. Recall that to x, y that satisfy all equations
More informationName Date Class California Standards 17.0, Quadratic Equations and Functions. Step 2: Graph the points. Plot the ordered pairs from your table.
California Standards 17.0, 1.0 9-1 There are three steps to graphing a quadratic function. Graph y x 3. Quadratic Equations and Functions 6 y 6 y x y x 3 5 1 1 0 3 1 1 5 0 x 0 x Step 1: Make a table of
More informationCC Algebra Quadratic Functions Test Review. 1. The graph of the equation y = x 2 is shown below. 4. Which parabola has an axis of symmetry of x = 1?
Name: CC Algebra Quadratic Functions Test Review Date: 1. The graph of the equation y = x 2 is shown below. 4. Which parabola has an axis of symmetry of x = 1? a. c. c. b. d. Which statement best describes
More informationFinal Exam Review for DMAT 0310
Final Exam Review for DMAT 010 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Factor the polynomial completely. What is one of the factors? 1) x
More information; Vertex: ( b. 576 feet above the ground?
Lesson 8: Applications of Quadratics Quadratic Formula: x = b± b 2 4ac 2a ; Vertex: ( b, f ( b )) 2a 2a Standard: F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand
More informationSolving Quadratic Equations: Algebraically and Graphically Read 3.1 / Examples 1 4
CC Algebra II HW #14 Name Period Row Date Solving Quadratic Equations: Algebraically and Graphically Read 3.1 / Examples 1 4 Section 3.1 In Exercises 3 12, solve the equation by graphing. (See Example
More informationThe Quadratic Formula. ax 2 bx c 0 where a 0. Deriving the Quadratic Formula. Isolate the constant on the right side of the equation.
SECTION 11.2 11.2 The Quadratic Formula 11.2 OBJECTIVES 1. Solve quadratic equations by using the quadratic formula 2. Determine the nature of the solutions of a quadratic equation by using the discriminant
More informationChapter 1 Notes: Quadratic Functions
19 Chapter 1 Notes: Quadratic Functions (Textbook Lessons 1.1 1.2) Graphing Quadratic Function A function defined by an equation of the form, The graph is a U-shape called a. Standard Form Vertex Form
More informationAlgebra II Unit #2 4.6 NOTES: Solving Quadratic Equations (More Methods) Block:
Algebra II Unit # Name: 4.6 NOTES: Solving Quadratic Equations (More Methods) Block: (A) Background Skills - Simplifying Radicals To simplify a radical that is not a perfect square: 50 8 300 7 7 98 (B)
More informationFoundations of Math II Unit 5: Solving Equations
Foundations of Math II Unit 5: Solving Equations Academics High School Mathematics 5.1 Warm Up Solving Linear Equations Using Graphing, Tables, and Algebraic Properties On the graph below, graph the following
More informationCHAPTER 1 QUADRATIC FUNCTIONS AND FACTORING
CHAPTER 1 QUADRATIC FUNCTIONS AND FACTORING Big IDEAS: 1) Graphing and writing quadratic functions in several forms ) Solving quadratic equations using a variety of methods 3) Performing operations with
More informationUnit 7 Quadratic Functions
Algebra I Revised 11/16 Unit 7 Quadratic Functions Name: 1 CONTENTS 9.1 Graphing Quadratic Functions 9.2 Solving Quadratic Equations by Graphing 9.1 9.2 Assessment 8.6 Solving x^2+bx+c=0 8.7 Solving ax^2+bx+c=0
More information= 9 = x + 8 = = -5x 19. For today: 2.5 (Review) and. 4.4a (also review) Objectives:
Math 65 / Notes & Practice #1 / 20 points / Due. / Name: Home Work Practice: Simplify the following expressions by reducing the fractions: 16 = 4 = 8xy =? = 9 40 32 38x 64 16 Solve the following equations
More information6.1 Quadratic Expressions, Rectangles, and Squares. 1. What does the word quadratic refer to? 2. What is the general quadratic expression?
Advanced Algebra Chapter 6 - Note Taking Guidelines Complete each Now try problem in your notes and work the problem 6.1 Quadratic Expressions, Rectangles, and Squares 1. What does the word quadratic refer
More informationQuadratic Functions. Key Terms. Slide 1 / 200. Slide 2 / 200. Slide 3 / 200. Table of Contents
Slide 1 / 200 Quadratic Functions Table of Contents Key Terms Identify Quadratic Functions Explain Characteristics of Quadratic Functions Solve Quadratic Equations by Graphing Solve Quadratic Equations
More informationQuadratic Functions. Key Terms. Slide 2 / 200. Slide 1 / 200. Slide 3 / 200. Slide 4 / 200. Slide 6 / 200. Slide 5 / 200.
Slide 1 / 200 Quadratic Functions Slide 2 / 200 Table of Contents Key Terms Identify Quadratic Functions Explain Characteristics of Quadratic Functions Solve Quadratic Equations by Graphing Solve Quadratic
More informationSlide 1 / 200. Quadratic Functions
Slide 1 / 200 Quadratic Functions Key Terms Slide 2 / 200 Table of Contents Identify Quadratic Functions Explain Characteristics of Quadratic Functions Solve Quadratic Equations by Graphing Solve Quadratic
More informationMay 16, Aim: To review for Quadratic Function Exam #2 Homework: Study Review Materials. Warm Up - Solve using factoring: 5x 2 + 7x + 2 = 0
Aim: To review for Quadratic Function Exam #2 Homework: Study Review Materials Warm Up - Solve using factoring: 5x 2 + 7x + 2 = 0 Review Topic Index 1. Consecutive Integer Word Problems 2. Pythagorean
More informationUnit 2 Day 7. Quadratic Formula & the Discriminant
Unit Day 7 Quadratic Formula & the Discriminant 1 Warm Up Day 7 1. Solve each of the quadratic functions by graphing and algebraic reasoning: a. x 3 = 0 b. x + 5x 8 = 0 c. Explain why having alternative
More information2 P a g e. Essential Questions:
NC Math 1 Unit 5 Quadratic Functions Main Concepts Study Guide & Vocabulary Classifying, Adding, & Subtracting Polynomials Multiplying Polynomials Factoring Polynomials Review of Multiplying and Factoring
More information9-4. Quadratics and Projectiles. Vocabulary. Equations for the Paths of Projectiles. Activity. Lesson
Chapter 9 Lesson 9-4 Quadratics and Projectiles Vocabulary force of gravity initial upward velocity initial height BIG IDEA Assuming constant gravity, both the path of a projectile and the height of a
More information2.1 Quadratic Functions
Date:.1 Quadratic Functions Precalculus Notes: Unit Polynomial Functions Objective: The student will sketch the graph of a quadratic equation. The student will write the equation of a quadratic function.
More information2. Write each number as a power of 10 using negative exponents.
Q Review 1. Simplify each expression. a. 1 0 b. 5 2 1 c. d. e. (7) 2 f. 6 1 g. 6 0 h. (12x) 2 i. 1 j. 6bc 0 0 8 k. (11x) 0 l. 2 2 9 m. m 8 p 0 n. 5a 2c k ( mn) o. p. 8 p 2m n q. 8 2 q r 5 r. (10a) b 0
More informationUnit 9 Linear, Quadratic, Absolute Value Functions P a g e 1 Unit 9 Assignment 1 Graphing Inequalities of Linear, Quadratic, and Step Functions
Unit 9 Linear, Quadratic, Absolute Value Functions P a g e 1 Unit 9 Assignment 1 Graphing Inequalities of Linear, Quadratic, and Step Functions Directions: WITHOUT THE CALCULATOR, graph the inequalities
More information. State the important connection between the coefficients of the given trinomials and the values you found for r.
Motivational Problems on Quadratics 1 1. Factor the following perfect-square trinomials : (a) x 1x 36 (b) x 14x 49 (c) x 0x 100 As suggested, these should all look like either ( x r) or ( x r). State the
More informationThe Quadratic Formula, the Discriminant, and Solving Quadratic Equations and Inequalities
CHAPTER The Quadratic Formula, the Discriminant, and Solving Quadratic Equations and Inequalities 009 Carnegie Learning, Inc. The Chinese invented rockets over 700 years ago. Since then rockets have been
More information- a function that can be written in the standard form. - a form of a parabola where and (h, k) is the vertex
4-1 Quadratic Functions and Equations Objectives A2.A.REI.D.6 (formerly A-REI.D.11) Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the
More information3.4 Solving Quadratic Equations by Completing
www.ck1.org Chapter 3. Quadratic Equations and Quadratic Functions 3.4 Solving Quadratic Equations by Completing the Square Learning objectives Complete the square of a quadratic expression. Solve quadratic
More informationFall 09/MAT 140/Worksheet 1 Name: Show all your work. 1. (6pts) Simplify and write the answer so all exponents are positive:
Fall 09/MAT 140/Worksheet 1 Name: Show all your work. 1. (6pts) Simplify and write the answer so all exponents are positive: a) (x 3 y 6 ) 3 x 4 y 5 = b) 4x 2 (3y) 2 (6x 3 y 4 ) 2 = 2. (2pts) Convert to
More informationCommon Core Algebra 2. Chapter 3: Quadratic Equations & Complex Numbers
Common Core Algebra 2 Chapter 3: Quadratic Equations & Complex Numbers 1 Chapter Summary: The strategies presented for solving quadratic equations in this chapter were introduced at the end of Algebra.
More informationQuadratic Functions and Equations
Quadratic Functions and Equations Quadratic Graphs and Their Properties Objective: To graph quadratic functions of the form y = ax 2 and y = ax 2 + c. Objectives I can identify a vertex. I can grapy y
More informationFor Your Notebook E XAMPLE 1. Factor when b and c are positive KEY CONCEPT. CHECK (x 1 9)(x 1 2) 5 x 2 1 2x 1 9x Factoring x 2 1 bx 1 c
9.5 Factor x2 1 bx 1 c Before You factored out the greatest common monomial factor. Now You will factor trinomials of the form x 2 1 bx 1 c. Why So you can find the dimensions of figures, as in Ex. 61.
More informationQuadratic Applications Name: Block: 3. The product of two consecutive odd integers is equal to 30 more than the first. Find the integers.
Quadratic Applications Name: Block: This problem packet is due before 4pm on Friday, October 26. It is a formative assessment and worth 20 points. Complete the following problems. Circle or box your answer.
More informationSolutions Key Quadratic Functions
CHAPTER 5 Solutions Key Quadratic Functions ARE YOU READY? PAGE 11 1. E. C. A. B 5. (.) (.)(.) 10. 6. ( 5) ( 5 )( 5 ) 5 7. 11 11 8. 1 16 1 9. 7 6 6 11. 75 75 5 11 15 11 1. (x - )(x - 6) x - 6x - x + 1
More informationAlgebra I. Slide 1 / 175. Slide 2 / 175. Slide 3 / 175. Quadratics. Table of Contents Key Terms
Slide 1 / 175 Slide 2 / 175 Algebra I Quadratics 2015-11-04 www.njctl.org Key Terms Table of Contents Click on the topic to go to that section Slide 3 / 175 Characteristics of Quadratic Equations Transforming
More informationAlgebra I. Key Terms. Slide 1 / 175 Slide 2 / 175. Slide 3 / 175. Slide 4 / 175. Slide 5 / 175. Slide 6 / 175. Quadratics.
Slide 1 / 175 Slide / 175 Algebra I Quadratics 015-11-04 www.njctl.org Key Terms Slide 3 / 175 Table of Contents Click on the topic to go to that section Slide 4 / 175 Characteristics of Quadratic Equations
More informationName Class Date. Identify the vertex of each graph. Tell whether it is a minimum or a maximum.
Practice Quadratic Graphs and Their Properties Identify the verte of each graph. Tell whether it is a minimum or a maimum. 1. y 2. y 3. 2 4 2 4 2 2 y 4 2 2 2 4 Graph each function. 4. f () = 3 2 5. f ()
More informationUNIT 3: MODELING AND ANALYZING QUADRATIC FUNCTIONS
UNIT 3: MODELING AND ANALYZING QUADRATIC FUNCTIONS This unit investigates quadratic functions. Students study the structure of quadratic expressions and write quadratic expressions in equivalent forms.
More information2 If ax + bx + c = 0, then x = b) What are the x-intercepts of the graph or the real roots of f(x)? Round to 4 decimal places.
Quadratic Formula - Key Background: So far in this course we have solved quadratic equations by the square root method and the factoring method. Each of these methods has its strengths and limitations.
More informationAlgebra I Quadratics
1 Algebra I Quadratics 2015-11-04 www.njctl.org 2 Key Terms Table of Contents Click on the topic to go to that section Characteristics of Quadratic Equations Transforming Quadratic Equations Graphing Quadratic
More informationSubtract 16 from both sides. Divide both sides by 9. b. Will the swing touch the ground? Explain how you know.
REVIEW EXAMPLES 1) Solve 9x + 16 = 0 for x. 9x + 16 = 0 9x = 16 Original equation. Subtract 16 from both sides. 16 x 9 Divide both sides by 9. 16 x Take the square root of both sides. 9 4 x i 3 Evaluate.
More informationPart I: SCIENTIFIC CALCULATOR REQUIRED. 1. [6 points] Compute each number rounded to 3 decimal places. Please double check your answer.
Chapter 1 Sample Pretest Part I: SCIENTIFIC CALCULATOR REQUIRED 1. [6 points] Compute each number rounded to 3 decimal places. Please double check your answer. 3 2+3 π2 +7 (a) (b) π 1.3+ 7 Part II: NO
More informationy ax bx c OR 0 then either a = 0 OR b = 0 Steps: 1) if already factored, set each factor in ( ) = 0 and solve
Algebra 1 SOL Review: Quadratics Name 67B Solving Quadratic equations using Zero-Product Property. Quadratic equation: ax bx c 0 OR y ax bx c OR f ( x ) ax bx c Zero-Product Property: if a b 0 then either
More informationSolving Quadratic Equations Review
Math III Unit 2: Polynomials Notes 2-1 Quadratic Equations Solving Quadratic Equations Review Name: Date: Period: Some quadratic equations can be solved by. Others can be solved just by using. ANY quadratic
More information3.4 The Fundamental Theorem of Algebra
333371_0304.qxp 12/27/06 1:28 PM Page 291 3.4 The Fundamental Theorem of Algebra Section 3.4 The Fundamental Theorem of Algebra 291 The Fundamental Theorem of Algebra You know that an nth-degree polynomial
More informationGraphing Quadratics Algebra 10.0
Graphing Quadratics Algebra 10.0 Quadratic Equations and Functions: y 7 5 y 5 1 f ( ) ( 3) 6 Once again, we will begin by graphing quadratics using a table of values. Eamples: Graph each using the domain
More information(a) Write down the value of q and of r. (2) Write down the equation of the axis of symmetry. (1) (c) Find the value of p. (3) (Total 6 marks)
1. Let f(x) = p(x q)(x r). Part of the graph of f is shown below. The graph passes through the points ( 2, 0), (0, 4) and (4, 0). (a) Write down the value of q and of r. (b) Write down the equation of
More informationAcquisition Lesson Planning Form Key Standards addressed in this Lesson: MM2A4b & MM2A4c Time allotted for this Lesson: 9 hours
Acquisition Lesson Planning Form Key Standards addressed in this Lesson: MM2A4b & MM2A4c Time allotted for this Lesson: 9 hours Essential Question: LESSON 3 Solving Quadratic Equations and Inequalities
More informationRoots are: Solving Quadratics. Graph: y = 2x 2 2 y = x 2 x 12 y = x 2 + 6x + 9 y = x 2 + 6x + 3. real, rational. real, rational. real, rational, equal
Solving Quadratics Graph: y = 2x 2 2 y = x 2 x 12 y = x 2 + 6x + 9 y = x 2 + 6x + 3 Roots are: real, rational real, rational real, rational, equal real, irrational 1 To find the roots algebraically, make
More informationMaintaining Mathematical Proficiency
Chapter Maintaining Mathematical Proficiency Simplify the expression. 1. 8x 9x 2. 25r 5 7r r + 3. 3 ( 3x 5) + + x. 3y ( 2y 5) + 11 5. 3( h 7) 7( 10 h) 2 2 +. 5 8x + 5x + 8x Find the volume or surface area
More informationUnit 3: HW3.5 Sum and Product
Unit 3: HW3.5 Sum and Product Without solving, find the sum and product of the roots of each equation. 1. x 2 8x + 7 = 0 2. 2x + 5 = x 2 3. -7x + 4 = -3x 2 4. -10x 2 = 5x - 2 5. 5x 2 2x 3 4 6. 1 3 x2 3x
More informationExponent Laws. a m a n = a m + n a m a n = a m n, a 0. ( ab) m = a m b m. ˆ m. = a m. a n = 1 a n, a 0. n n = a. Radicals. m a. n b Ë. m a. = mn.
Name:. Math 0- Formula Sheet Sequences and Series t n = t + ( n )d S n = n È t ÎÍ + ( n )d S n = n Ê Á t + t n ˆ t n = t r n Ê t r n ˆ Á S n =, r r S n = rt n t r, r S = t r, r Trigonometry Exponent Laws
More informationChapter 9 Quadratic Graphs
Chapter 9 Quadratic Graphs Lesson 1: Graphing Quadratic Functions Lesson 2: Vertex Form & Shifts Lesson 3: Quadratic Modeling Lesson 4: Focus and Directrix Lesson 5: Equations of Circles and Systems Lesson
More information1. The graph of a quadratic function is shown. Each square is one unit.
1. The graph of a quadratic function is shown. Each square is one unit. a. What is the vertex of the function? b. If the lead coefficient (the value of a) is 1, write the formula for the function in vertex
More informationMath 110 Final Exam Review Revised December 2015
Math 110 Final Exam Review Revised December 2015 Factor out the GCF from each polynomial. 1) 60x - 15 2) 7x 8 y + 42x 6 3) x 9 y 5 - x 9 y 4 + x 7 y 2 - x 6 y 2 Factor each four-term polynomial by grouping.
More informationMath 110 Final Exam Review Revised October 2018
Math 110 Final Exam Review Revised October 2018 Factor out the GCF from each polynomial. 1) 60x - 15 2) 7x 8 y + 42x 6 3) x 9 y 5 - x 9 y 4 + x 7 y 2 - x 6 y 2 Factor each four-term polynomial by grouping.
More informationTest 4 also includes review problems from earlier sections so study test reviews 1, 2, and 3 also.
MATD 0370 ELEMENTARY ALGEBRA REVIEW FOR TEST 4 (1.1-10.1, not including 8.2) Test 4 also includes review problems from earlier sections so study test reviews 1, 2, and 3 also. 1. Factor completely: a 2
More information3 UNIT 4: QUADRATIC FUNCTIONS -- NO CALCULATOR
Name: Algebra Final Exam Review, Part 3 UNIT 4: QUADRATIC FUNCTIONS -- NO CALCULATOR. Solve each of the following equations. Show your steps and find all solutions. a. 3x + 5x = 0 b. x + 5x - 9 = x + c.
More informationAlgebra II Honors Unit 3 Assessment Review Quadratic Functions. Formula Box. f ( x) 2 x 3 25 from the parent graph of
Name: Algebra II Honors Unit 3 Assessment Review Quadratic Functions Date: Formula Box x = b a x = b ± b 4ac a h 6t h 0 ) What are the solutions of x 3 5? x 8or x ) Describe the transformation of f ( x)
More information5-6. Quadratic Equations. Zero-Product Property VOCABULARY TEKS FOCUS ESSENTIAL UNDERSTANDING. Problem 1. Solving a Quadratic Equation by Factoring
5-6 Quadratic Equations TEKS FOCUS TEKS (4)(F) Solve quadratic and square root equations. TEKS (1)(C) Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate,
More informationThe x-coordinate of the vertex: The equation of the axis of symmetry:
Algebra 2 Notes Section 4.1: Graph Quadratic Functions in Standard Form Objective(s): Vocabulary: I. Quadratic Function: II. Standard Form: III. Parabola: IV. Parent Function for Quadratic Functions: Vertex
More informationWhen a is positive, the parabola opens up and has a minimum When a is negative, the parabola opens down and has a maximum
KEY CONCEPTS For a quadratic relation of the form y = ax 2 + c, the maximum or minimum value occurs at c, which is the y-intercept. When a is positive, the parabola opens up and has a minimum When a is
More informationWhen factoring, we ALWAYS start with the (unless it s 1).
Math 100 Elementary Algebra Sec 5.1: The Greatest Common Factor and Factor By Grouping (FBG) Recall: In the product XY, X and Y are factors. Defn In an expression, any factor that is common to each term
More informationUnit 5 Test: 9.1 Quadratic Graphs and Their Properties
Unit 5 Test: 9.1 Quadratic Graphs and Their Properties Quadratic Equation: (Also called PARABOLAS) 1. of the STANDARD form y = ax 2 + bx + c 2. a, b, c are all real numbers and a 0 3. Always have an x
More informationFree Response Questions Compiled by Kaye Autrey for face-to-face student instruction in the AP Calculus classroom
Free Response Questions 1969-010 Compiled by Kaye Autrey for face-to-face student instruction in the AP Calculus classroom 1 AP Calculus Free-Response Questions 1969 AB 1 Consider the following functions
More informationRemember, you may not use a calculator when you take the assessment test.
Elementary Algebra problems you can use for practice. Remember, you may not use a calculator when you take the assessment test. Use these problems to help you get up to speed. Perform the indicated operation.
More informationEX: Simplify the expression. EX: Simplify the expression. EX: Simplify the expression
SIMPLIFYING RADICALS EX: Simplify the expression 84x 4 y 3 1.) Start by creating a factor tree for the constant. In this case 84. Keep factoring until all of your nodes are prime. Two factor trees are
More informationMATH 121: EXTRA PRACTICE FOR TEST 2. Disclaimer: Any material covered in class and/or assigned for homework is a fair game for the exam.
MATH 121: EXTRA PRACTICE FOR TEST 2 Disclaimer: Any material covered in class and/or assigned for homework is a fair game for the exam. 1 Linear Functions 1. Consider the functions f(x) = 3x + 5 and g(x)
More informationSpring 06/MAT 140/Worksheet 1 Name: Show all your work.
Spring 06/MAT 140/Worksheet 1 Name: Show all your work. 1. (4pts) Write two examples of each kind of number: natural integer rational irrational 2. (12pts) Simplify: ( a) 3 4 2 + 4 2 ) = 3 b) 3 20 7 15
More informationMATH 121: EXTRA PRACTICE FOR TEST 2. Disclaimer: Any material covered in class and/or assigned for homework is a fair game for the exam.
MATH 121: EXTRA PRACTICE FOR TEST 2 Disclaimer: Any material covered in class and/or assigned for homework is a fair game for the exam. 1 Linear Functions 1. Consider the functions f(x) = 3x + 5 and g(x)
More informationUsing Properties of Exponents
6.1 Using Properties of Exponents Goals p Use properties of exponents to evaluate and simplify expressions involving powers. p Use exponents and scientific notation to solve real-life problems. VOCABULARY
More informationMs. Peralta s IM3 HW 5.4. HW 5.4 Solving Quadratic Equations. Solve the following exercises. Use factoring and/or the quadratic formula.
HW 5.4 HW 5.4 Solving Quadratic Equations Name: Solve the following exercises. Use factoring and/or the quadratic formula. 1. 2. 3. 4. HW 5.4 5. 6. 4x 2 20x + 25 = 36 7. 8. HW 5.4 9. 10. 11. 75x 2 30x
More informationLesson 7.1 Polynomial Degree and Finite Differences
Lesson 7.1 Polynomial Degree and Finite Differences 1. Identify the degree of each polynomial. a. 3x 4 2x 3 3x 2 x 7 b. x 1 c. 0.2x 1.x 2 3.2x 3 d. 20 16x 2 20x e. x x 2 x 3 x 4 x f. x 2 6x 2x 6 3x 4 8
More informationSolve Quadratic Equations by Completing the Square
10.5 Solve Quadratic Equations by Completing the Square Before You solved quadratic equations by finding square roots. Now You will solve quadratic equations by completing the square. Why? So you can solve
More information1) Explain in complete sentences how to solve the following equation using the factoring method. Y=7x
TEST 13 REVIEW Quadratics 1) Explain in complete sentences how to solve the following equation using the factoring method. Y=7x 2 +28. 2) Find the domain and range if the points in the table are discrete
More informationUnit: Solving Quadratic Equations
Unit: Solving Quadratic Equations Name Dates Taught Outcome 11P.R.1. Factor polynomial expressions of the of the form o ax 2 - bx +c = 0, a 0 o a 2 x 2 b 2 y 2 - c = 0, a 0 b 0 o a(f(x)) 2 b(f(x))x +c
More informationSkills Practice Skills Practice for Lesson 3.1
Skills Practice Skills Practice for Lesson. Name Date Lots and Projectiles Introduction to Quadratic Functions Vocabular Define each term in our own words.. quadratic function. vertical motion Problem
More information1. Graph (on graph paper) the following equations by creating a table and plotting points on a coordinate grid y = -2x 2 4x + 2 x y.
1. Graph (on graph paper) the following equations by creating a table and plotting points on a coordinate grid y = -2x 2 4x + 2 x y y = x 2 + 6x -3 x y domain= range= -4-3 -2-1 0 1 2 3 4 domain= range=
More informationSolving Quadratic Equations (Adapted from Core Plus Mathematics, Courses 1 and 2)
Solving Quadratic Equations (Adapted from Core Plus Mathematics, Courses 1 and ) In situations that involve quadratic functions, the interesting questions often require solving equations. For example,
More informationSolving Multi-Step Equations
1. Clear parentheses using the distributive property. 2. Combine like terms within each side of the equal sign. Solving Multi-Step Equations 3. Add/subtract terms to both sides of the equation to get the
More informationQuadratic Functions and Equations
Quadratic Functions and Equations 9A Quadratic Functions 9-1 Quadratic Equations and Functions Lab Explore the Axis of Symmetry 9- Characteristics of Quadratic Functions 9-3 Graphing Quadratic Functions
More informationChapter Four Notes N P U2C4
Chapter Four Notes N P U2C4 Name Period Section 4.3: Quadratic Functions and Their Properties Recall from Chapter Three as well as advanced algebra that a quadratic function (or square function, as it
More informationx and y, called the coordinates of the point.
P.1 The Cartesian Plane The Cartesian Plane The Cartesian Plane (also called the rectangular coordinate system) is the plane that allows you to represent ordered pairs of real numbers by points. It is
More informationMAT 107 College Algebra Fall 2013 Name. Final Exam, Version X
MAT 107 College Algebra Fall 013 Name Final Exam, Version X EKU ID Instructor Part 1: No calculators are allowed on this section. Show all work on your paper. Circle your answer. Each question is worth
More informationUnit 3. Expressions and Equations. 118 Jordan School District
Unit 3 Epressions and Equations 118 Unit 3 Cluster 1 (A.SSE.): Interpret the Structure of Epressions Cluster 1: Interpret the structure of epressions 3.1. Recognize functions that are quadratic in nature
More informationQuadratic Word Problems - Develop an Approach and Solve
Name: Class: Date: ID: A Quadratic Word Problems - Develop an Approach and Solve Short Answer 1. Suppose you have 54 feet of fencing to enclose a rectangular dog pen. The function A = 7x x, where x = width,
More information( )( ) Algebra I / Technical Algebra. (This can be read: given n elements, choose r, 5! 5 4 3! ! ( 5 3 )! 3!(2) 2
470 Algebra I / Technical Algebra Absolute Value: A number s distance from zero on a number line. A number s absolute value is nonnegative. 4 = 4 = 4 Algebraic Expressions: A mathematical phrase that can
More informationAP Calculus Free-Response Questions 1969-present AB
AP Calculus Free-Response Questions 1969-present AB 1969 1. Consider the following functions defined for all x: f 1 (x) = x, f (x) = xcos x, f 3 (x) = 3e x, f 4 (x) = x - x. Answer the following questions
More informationMore applications of quadratic functions
Algebra More applications of quadratic functions Name: There are many applications of quadratic functions in the real world. We have already considered applications for which we were given formulas and
More informationlsolve. 25(x + 3)2-2 = 0
II nrm!: lsolve. 25(x + 3)2-2 = 0 ISolve. 4(x - 7) 2-5 = 0 Isolate the squared term. Move everything but the term being squared to the opposite side of the equal sign. Use opposite operations. Isolate
More informationAlgebra 1. Math Review Packet. Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals
Algebra 1 Math Review Packet Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals 2017 Math in the Middle 1. Clear parentheses using the distributive
More informationCollege Algebra Joysheet 1 MAT 140, Fall 2015 D. Ivanšić. Name: Simplify and write the answer so all exponents are positive:
College Algebra Joysheet 1 MAT 140, Fall 2015 D. Ivanšić Name: Covers: R.1 R.4 Show all your work! Simplify and write the answer so all exponents are positive: 1. (5pts) (3x 4 y 2 ) 2 (5x 2 y 6 ) 3 = 2.
More informationSect Polynomial and Rational Inequalities
158 Sect 10.2 - Polynomial and Rational Inequalities Concept #1 Solving Inequalities Graphically Definition A Quadratic Inequality is an inequality that can be written in one of the following forms: ax
More informationMAT 135. In Class Assignments
MAT 15 In Class Assignments 1 Chapter 1 1. Simplify each expression: a) 5 b) (5 ) c) 4 d )0 6 4. a)factor 4,56 into the product of prime factors b) Reduce 4,56 5,148 to lowest terms.. Translate each statement
More informationAlgebra B Chapter 9 Unit Test Version 1 of 3
Name Per. _ Date Algebra B Chapter 9 Unit Test Version 1 of 3 Instructions: 1. Reduce all radicals to simplest terms. Do not approximate square roots as decimals. 2. Place your name, period and the date
More informationx (vertex is halfway between the x-intercepts)
Big Idea: A quadratic equation in the form a b c 0 has a related function f ( ) a b c. The zeros of the function are the -intercepts of its graph. These -values are the solutions or roots of the related
More informationS4 (4.3) Quadratic Functions.notebook February 06, 2018
Daily Practice 2.11.2017 Q1. Multiply out and simplify 3g - 5(2g + 4) Q2. Simplify Q3. Write with a rational denominator Today we will be learning about quadratic functions and their graphs. Q4. State
More informationThe Graph of a Quadratic Function. Quadratic Functions & Models. The Graph of a Quadratic Function. The Graph of a Quadratic Function
8/1/015 The Graph of a Quadratic Function Quadratic Functions & Models Precalculus.1 The Graph of a Quadratic Function The Graph of a Quadratic Function All parabolas are symmetric with respect to a line
More information2-7 Solving Quadratic Inequalities. ax 2 + bx + c > 0 (a 0)
Quadratic Inequalities In One Variable LOOKS LIKE a quadratic equation but Doesn t have an equal sign (=) Has an inequality sign (>,
More information