Unit 5 Test: 9.1 Quadratic Graphs and Their Properties
|
|
- Terence Welch
- 6 years ago
- Views:
Transcription
1 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 2 How do we determine which way it opens? -if leading coefficient a is positive, it opens up Ex: y = 3x 2 +2x -5 - if leading coefficient a is negative it opens down Ex: y = -4x 2 +3x -10 Maximum/Minimum Point (x, y) Depends on opening It is the VERTEX Axis of Symmetry vertical line drawn through middle of graph, you can fold one half onto other b USE: x = to state the EQUATION. 2a FINDING VERTEX AND AXIS OF SYMMETRY Label what a, b and c are equal too Axis of Symmetry: (x = #) Vertex: (x, y) b b 1) Plug into x = 1) Plug into x = 2a 2a 2) Simplify the right side 2) Simplify the right side 3) Leave answer as an equation 3) Plug into the quadratic to find y 4) Write answer as (x, y) Example: For the following, state the vertex, axis of symmetry and if it s a max or min value. 1) y = 2x 2 + 4x - 6 2) y = x 2 6 1
2 3) 4) y = -3x 2 6x + 2 5) y = -2x 2 6) y = -2x 2 + 2x - 3 2
3 9.2: Graphing Quadratic Functions Steps to Graph 1) List out a, b and c 2) Find the vertex 3) Choose x values above the vertex and below it 4) Make a t-chart and fill 5) Graph the points Examples: Graph the following quadratic functions. State the axis of symmetry and the coordinates of the vertex. Graph the axis of symmetry along with the quadratic. 1) y = -3x x + 1 2) f(x) = 2x 2 + 4x - 1 y y x x 3
4 Story Problem Applications: During Halftime of a basketball game, a sling shot launches T-shirts in the crowd hitting spectators in the head. A t-shirt has a velocity of 72 ft/s. It is caught 35 ft above the court. How long will it take the t-shirt to reach its maximum height? What is the maximum height? The function h = -16t 2 +72t + 5 gives the t-shirts height after t seconds. Suppose a tennis player hits a ball over the net. The ball leaves the racket 0.5m above the ground. The equation h = -4.9t t gives the ball s height h in meters after t seconds. When will the ball be at its highest point in this path? Rounds your answer to the nearest tenth? 4
5 9.3: Solving Quadratic Equations: Day 1 WHAT DOES THIS ALL MEAN?? Roots/Solutions/X-intercepts are all the same thing.where it crosses the x-axis!!!! What are all the ways to solve quadratics? 1) Solve by graphing. (Only works if they cross at specific points.) 2) Solve by factoring. (Must factor by grouping and not everything is factorable.) 3) Solve by graphing calculator. (Only applies if they cross at specific points.) 4) Solve by square roots. (Only works is there is no x term or you factor to something squared) 5) QUADRATIC FORMULA (Works for every situation) 5
6 Square Root Property If you isolate the x 2, you can use this to solve. Remember x 2 = 9 means what number times itself equals 9. YOU MUST INCLUDE POSITIVE AND NEGATIVE NUMBERS!!!! Example: x 2 81 = 0 x 2 = 81 Isolate the x 2 x = Take the square root of each side Remember to include positive and negative Examples: Solve the following quadratics. 1) x 2 = 64 2) w 2 36 = 64 3) 3x = 0 4) (x - 4) 2 = 25 Examples: Find the roots of the following quadratics. Round to the nearest 10 th. 1) x 2 25 = 0 2) x 2 + 6x -7 = 0 3) x = 0 6
7 9.4: Solve Quadratics: Day 2 Graphing works best when the graph is given to you. Square roots work best when you have no bx term. Examples: What are the solutions of each equation? 1) (t 5)(t + 7) = 0 2) (2x + 3)(x 4) = 0 3) x(x + 4) = 0 Using factoring to solve equations Steps: 1) Make the equation equal to zero 2) Make certain it is in the form x 2 + bx + c (Standard form of a quadratic) 3) Factor the trinomial after getting it to equal zero (Factor by Grouping) 4) Apply the zero product property from above and solve 7
8 Examples: Solve the following and check you solutions. Round to the nearest 10 th. 4) x 2 + 5x + 6 = 0 5) x 2-6x = - 8 6) 4x 2-21x - 18 = 0 7) x 2 = 4x Story Problem: 8) You are constructing a frame for the rectangular photo shown. You want the frame to be the same width all the way around and the total area of the frame and photo should be 315in 2. What should the outer dimensions of the frame be? 8
9 9.4: Solve Quadratics: Day 3 Examples: What are the solutions of the following? Round to the nearest 10 th. 1) x 2-6x = 247 2) x 2 + 6x = 216 3) x 2 + 9x + 15 = 0 4) x 2 14x + 16 = 0 **5) 3x 2 + 8x 96 = 0 Example: You are planning a flower garden consisting of 3 square plots surrounded by a 1-ft border. The total area of the garden and the border is 100 ft 2. What is the side length of each square plot? 9
10 10.2: Simplifying Radicals Examples: Simplify the following. 1) 2) 3) 4) Factor Tree Factor down completely Circle pairs of numbers Simplifying Radicals Biggest Perfect Square -- Find pairs of factors --Use product property Examples: Find the simplest form of the following expressions. 5) 6) 10
11 7) 8) 9) 10) #1 Rule: NO RADICAL IS ALLOWED IN THE DENOMINATOR!!!! You Must Rationalize to Remove it. Multiply top and bottom by the radical in the bottom and simplify. Examples: Simplify the following expressions. 11) ) ) 12 y 27 14) 11
12 9.6: The Quadratic Formula and Using The Discriminant - used to solve any quadratics or when you can t factor - slow down and work out every step - quadratic must be in standard form: ax 2 + bx + c = 0. Discriminant: Tells how many real solutions there are Solving using the formula: 1) Make sure it is in standard form 2) List out what a, b, and c all equal 3) Rewrite the formula using the values listed above 4) SLOW DOWN AND SOLVE FROM THE INSIDE OUT Examples: State the value of the discriminant and determine the number of real roots. 1) 2x x + 11 = 0 2) 4t 2 20t = -25 3) 3x 2 + 4x = -2 12
13 Examples: What are the solutions to the following quadratics. 4) x 2 2x 8 = 0 5) x 2 4x = 21 6) 2x 2 3x = -5 7) 4x x + 9 = 0 ALL OF THESE METHODS WILL SOLVE QUADRATICS. THE QUADRATIC FORMULA WILL WORK IN ANY SITUATION!!! 13
Quadratic 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 information4.1 Graphical Solutions of Quadratic Equations Date:
4.1 Graphical Solutions of Quadratic Equations Date: Key Ideas: Quadratic functions are written as f(x) = x 2 x 6 OR y = x 2 x 6. f(x) is f of x and means that the y value is dependent upon the value of
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 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 information3.1 Solving Quadratic Equations by Factoring
3.1 Solving Quadratic Equations by Factoring A function of degree (meaning the highest exponent on the variable is ) is called a Quadratic Function. Quadratic functions are written as, for example, f(x)
More information6.1 Solving Quadratic Equations by Factoring
6.1 Solving Quadratic Equations by Factoring A function of degree 2 (meaning the highest exponent on the variable is 2), is called a Quadratic Function. Quadratic functions are written as, for example,
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 informationSection 3.2 Quadratic Functions & Their Graphs
Week 2 Handout MAC 1140 Professor Niraj Wagh J Section 3.2 Quadratic Functions & Their Graphs Quadratic Function: Standard Form A quadratic function is a function that can be written in the form: f (x)
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 information= (Type exponential notation with positive exponents)
1. Subtract. Simplify by collecting like radical terms if possible. 2 2 = (Simplify your answer) 2. Add. Simplify if possible. = (Simplify your answer) 3. Divide and simplify. = (Type exponential notation
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 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 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 informationChapter 5 Smartboard Notes
Name Chapter 5 Smartboard Notes 10.1 Graph ax 2 + c Learning Outcome To graph simple quadratic functions Quadratic function A non linear function that can be written in the standard form y = ax 2 + bx
More informationSection 1.1. Chapter 1. Quadratics. Parabolas. Example. Example. ( ) = ax 2 + bx + c -2-1
Chapter 1 Quadratic Functions and Factoring Section 1.1 Graph Quadratic Functions in Standard Form Quadratics The polynomial form of a quadratic function is: f x The graph of a quadratic function is a
More informationUnit 3A: Factoring & Solving Quadratic Equations After completion of this unit, you will be able to
Unit 3A: Factoring & Solving Quadratic Equations After completion of this unit, you will be able to Learning Target #1: Factoring Factor the GCF out of a polynomial Factor a polynomial when a = 1 Factor
More informationHONORS GEOMETRY Summer Skills Set
HONORS GEOMETRY Summer Skills Set Algebra Concepts Adding and Subtracting Rational Numbers To add or subtract fractions with the same denominator, add or subtract the numerators and write the sum or difference
More informationChapter 4: Quadratic Functions and Factoring 4.1 Graphing Quadratic Functions in Stand
Chapter 4: Quadratic Functions and Factoring 4.1 Graphing Quadratic Functions in Stand VOCAB: a quadratic function in standard form is written y = ax 2 + bx + c, where a 0 A quadratic Function creates
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 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 informationChapter 9 Quadratic Functions and Equations
Chapter 9 Quadratic Functions and Equations 1 9 1Quadratic Graphs and their properties U shaped graph such as the one at the right is called a parabola. A parabola can open upward or downward. A parabola
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 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 informationSummer Work for students entering PreCalculus
Summer Work for students entering PreCalculus Name Directions: The following packet represent a review of topics you learned in Algebra 1, Geometry, and Algebra 2. Complete your summer packet on separate
More information2017 SUMMER REVIEW FOR STUDENTS ENTERING GEOMETRY
2017 SUMMER REVIEW FOR STUDENTS ENTERING GEOMETRY The following are topics that you will use in Geometry and should be retained throughout the summer. Please use this practice to review the topics you
More information9-8 Completing the Square
In the previous lesson, you solved quadratic equations by isolating x 2 and then using square roots. This method works if the quadratic equation, when written in standard form, is a perfect square. When
More informationLesson 9 Exploring Graphs of Quadratic Functions
Exploring Graphs of Quadratic Functions Graph the following system of linear inequalities: { y > 1 2 x 5 3x + 2y 14 a What are three points that are solutions to the system of inequalities? b Is the point
More information11.2 The Quadratic Formula
11.2 The Quadratic Formula Solving Quadratic Equations Using the Quadratic Formula. By solving the general quadratic equation ax 2 + bx + c = 0 using the method of completing the square, one can derive
More informationProperties of Graphs of Quadratic Functions
Properties of Graphs of Quadratic Functions y = ax 2 + bx + c 1) For a quadratic function given in standard form a tells us: c is the: 2) Given the equation, state the y-intercept and circle the direction
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 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 informationSummer Work for students entering PreCalculus
Summer Work for students entering PreCalculus Name Directions: The following packet represent a review of topics you learned in Algebra 1, Geometry, and Algebra 2. Complete your summer packet on separate
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 informationA. B. C. D. Quadratics Practice Test. Question 1. Select the graph of the quadratic function. g (x ) = 1 3 x 2. 3/8/2018 Print Assignment
Question 1. Select the graph of the quadratic function. g (x ) = 1 3 x 2 C. D. https://my.hrw.com/wwtb2/viewer/printall_vs23.html?umk5tfdnj31tcldd29v4nnzkclztk3w8q6wgvr262aca0a5fsymn1tfv8j1vs4qotwclvofjr8xhs0cldd29v4
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 information2. If the discriminant of a quadratic equation is zero, then there (A) are 2 imaginary roots (B) is 1 rational root
Academic Algebra II 1 st Semester Exam Mr. Pleacher Name I. Multiple Choice 1. Which is the solution of x 1 3x + 7? (A) x -4 (B) x 4 (C) x -4 (D) x 4. If the discriminant of a quadratic equation is zero,
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 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 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 informationName I.D. Number. Select the response that best completes the statement or answers the question.
Name I.D. Number Unit 4 Evaluation Evaluation 04 Second Year Algebra 1 (MTHH 039 059) This evaluation will cover the lessons in this unit. It is open book, meaning you can use your textbook, syllabus,
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 informationA2 HW Imaginary Numbers
Name: A2 HW Imaginary Numbers Rewrite the following in terms of i and in simplest form: 1) 100 2) 289 3) 15 4) 4 81 5) 5 12 6) -8 72 Rewrite the following as a radical: 7) 12i 8) 20i Solve for x in simplest
More informationChapter 16 Review. 1. What is the solution set of n 2 + 5n 14 = 0? (A) n = {0, 14} (B) n = { 1, 14} (C) n = { 2, 7} (D) n = { 2, 7} (E) n = { 7, 2}
Chapter 16 Review Directions: For each of the questions below, choose the best answer from the five choices given. 1. What is the solution set of n + 5n 14 = 0? (A) n = {0, 14} (B) n = { 1, 14} (C) n =
More informationAlgebra Quadratics Applications HW#54
Algebra Quadratics Applications HW#54 1: A science class designed a ball launcher and tested it by shooting a tennis ball up and off the top of a 15-story building. They determined that the motion of the
More informationSolving Quadratic Equations by Formula
Algebra Unit: 05 Lesson: 0 Complex Numbers All the quadratic equations solved to this point have had two real solutions or roots. In some cases, solutions involved a double root, but there were always
More informationPolynomials: Adding, Subtracting, & Multiplying (5.1 & 5.2)
Polynomials: Adding, Subtracting, & Multiplying (5.1 & 5.) Determine if the following functions are polynomials. If so, identify the degree, leading coefficient, and type of polynomial 5 3 1. f ( x) =
More informationQuadratic Function. Parabola. Parent quadratic function. Vertex. Axis of Symmetry
Name: Chapter 10: Quadratic Equations and Functions Section 10.1: Graph = a + c Quadratic Function Parabola Parent quadratic function Verte Ais of Smmetr Parent Function = - -1 0 1 1 Eample 1: Make a table,
More informationMath 2 1. Lesson 4-5: Completing the Square. When a=1 in a perfect square trinomial, then. On your own: a. x 2 18x + = b.
Math 1 Lesson 4-5: Completing the Square Targets: I can identify and complete perfect square trinomials. I can solve quadratic equations by Completing the Square. When a=1 in a perfect square trinomial,
More informationQUADRATIC FUNCTIONS AND MODELS
QUADRATIC FUNCTIONS AND MODELS What You Should Learn Analyze graphs of quadratic functions. Write quadratic functions in standard form and use the results to sketch graphs of functions. Find minimum and
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 informationAlgebra 2 Semester Test Review
Algebra 2 Semester Test Review Name This semester review covers everything from Semester 1. It is due. You will have a semester test that covers everything from the semester on. This packet is meant as
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 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 information9.3 Using the Quadratic Formula to Solve Equations
Name Class Date 9.3 Using the Quadratic Formula to Solve Equations Essential Question: What is the quadratic formula, and how can you use it to solve quadratic equations? Resource Locker Explore Deriving
More informationAlgebra II (Common Core) Summer Assignment Due: September 11, 2017 (First full day of classes) Ms. Vella
1 Algebra II (Common Core) Summer Assignment Due: September 11, 2017 (First full day of classes) Ms. Vella In this summer assignment, you will be reviewing important topics from Algebra I that are crucial
More informationB. Complex number have a Real part and an Imaginary part. 1. written as a + bi some Examples: 2+3i; 7+0i; 0+5i
Section 11.8 Complex Numbers I. The Complex Number system A. The number i = -1 1. 9 and 24 B. Complex number have a Real part and an Imaginary part II. Powers of i 1. written as a + bi some Examples: 2+3i;
More informationFor all questions, answer choice E. NOTA" means none of the above answers is correct.
For all questions, answer choice " means none of the above answers is correct. 1. The sum of the integers 1 through n can be modeled by a quadratic polynomial. What is the product of the non-zero coefficients
More informationAlgebra 1. Unit 3: Quadratic Functions. Romeo High School
Algebra 1 Unit 3: Quadratic Functions Romeo High School Contributors: Jennifer Boggio Jennifer Burnham Jim Cali Danielle Hart Robert Leitzel Kelly McNamara Mary Tarnowski Josh Tebeau RHS Mathematics Department
More informationSolving Quadratic Equations
Concepts: Solving Quadratic Equations, Completing the Square, The Quadratic Formula, Sketching Quadratics Solving Quadratic Equations Completing the Square ax + bx + c = a x + ba ) x + c Factor so the
More informationAlgebra Final Exam Review Packet
Algebra 1 00 Final Eam Review Packet UNIT 1 EXPONENTS / RADICALS Eponents Degree of a monomial: Add the degrees of all the in the monomial together. o Eample - Find the degree of 5 7 yz Degree of a polynomial:
More informationSection 5.4 Quadratic Functions
Math 150 c Lynch 1 of 6 Section 5.4 Quadratic Functions Definition. A quadratic function is one that can be written in the form, f(x) = ax 2 + bx + c, where a, b, and c are real numbers and a 0. This if
More informationAlgebra 2/Trig Apps: Chapter 5 Quadratics Packet
Algebra /Trig Apps: Chapter 5 Quadratics Packet In this unit we will: Determine what the parameters a, h, and k do in the vertex form of a quadratic equation Determine the properties (vertex, axis of symmetry,
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 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 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 informationQuadratic Equations. Math 20-1 Chapter 4. General Outcome: Develop algebraic and graphical reasoning through the study of relations.
Math 20-1 Chapter 4 Quadratic Equations General Outcome: Develop algebraic and graphical reasoning through the study of relations. Specific Outcomes: RF1. Factor polynomial expressions of the form: ax
More information30S Pre-Calculus Final Exam Review Chapters 1-4
30S Pre-Calculus Final Exam Review Chapters 1 - Name: 30S Pre-Calculus Final Exam Formula Sheet 30S Pre-Calculus Exam Review- Chapter 1 Sequences and Series Multiple Choice Identify the choice that best
More informationReview Notes - Solving Quadratic Equations
Review Notes - Solving Quadratic Equations What does solve mean? Methods for Solving Quadratic Equations: Solving by using Square Roots Solving by Factoring using the Zero Product Property Solving by Quadratic
More information6.4 6.notebook December 03, 2018
6.4 Opening Activity: 1. Expand and Simplify 3. Expand and Simplify (x 5) 2 y = (x 5) 2 3 2. Expand and Simplify 4. Expand and Simplify (x 5) 2 3 y + 3 = (x 5) 2 5. What is the vertex of the following
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 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 informationRegents Review Session #3 Functions
Regents Review Session #3 Functions A relation is a set of ordered pairs. A function is a relation in which each element of the domain corresponds t exactly one element in the range. (Each x value is paired
More informationSection 5.5 Complex Numbers
Name: Period: Section 5.5 Comple Numbers Objective(s): Perform operations with comple numbers. Essential Question: Tell whether the statement is true or false, and justify your answer. Every comple number
More informationSolving Quadratics Algebraically
Solving Quadratics Algebraically Table of Contents 1. Introduction to Solving Quadratics. Solving Quadratic Equations using Factoring 3. Solving Quadratic Equations in Context 4. Solving Quadratics using
More informationPre Calculus 11 Practice Midyear Exam 2014
Class: Date: Pre Calculus 11 Practice Midyear Exam 201 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following numbers occurs in the sequence
More informationUsing the Laws of Exponents to Simplify Rational Exponents
6. Explain Radicals and Rational Exponents - Notes Main Ideas/ Questions Essential Question: How do you simplify expressions with rational exponents? Notes/Examples What You Will Learn Evaluate and simplify
More informationUnit 5 Solving Quadratic Equations
SM Name: Period: Unit 5 Solving Quadratic Equations 5.1 Solving Quadratic Equations by Factoring Quadratic Equation: Any equation that can be written in the form a b c + + = 0, where a 0. Zero Product
More informationChapter 2 Polynomial and Rational Functions
SECTION.1 Linear and Quadratic Functions Chapter Polynomial and Rational Functions Section.1: Linear and Quadratic Functions Linear Functions Quadratic Functions Linear Functions Definition of a Linear
More informationAlgebra 2 Honors: Final Exam Review
Name: Class: Date: Algebra 2 Honors: Final Exam Review Directions: You may write on this review packet. Remember that this packet is similar to the questions that you will have on your final exam. Attempt
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 informationCHAPTER EIGHT: SOLVING QUADRATIC EQUATIONS Review April 9 Test April 17 The most important equations at this level of mathematics are quadratic
CHAPTER EIGHT: SOLVING QUADRATIC EQUATIONS Review April 9 Test April 17 The most important equations at this level of mathematics are quadratic equations. They can be solved using a graph, a perfect square,
More informationSolving Equations by Factoring. Solve the quadratic equation x 2 16 by factoring. We write the equation in standard form: x
11.1 E x a m p l e 1 714SECTION 11.1 OBJECTIVES 1. Solve quadratic equations by using the square root method 2. Solve quadratic equations by completing the square Here, we factor the quadratic member of
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 informationUnit 1 Review. To prove if a transformation preserves rigid motion, you can use the distance formula: Rules for transformations:
Unit 1 Review Function Notation A function is a mathematical relation so that every in the corresponds with one in the. To evaluate a function, f(x), substitute the for every x and calculate. Example:
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 informationUNIT #9 ROOTS AND IRRATIONAL NUMBERS REVIEW QUESTIONS
Answer Key Name: Date: UNIT #9 ROOTS AND IRRATIONAL NUMBERS REVIEW QUESTIONS Part I Questions. Which of the following is the value of 6? () 6 () 4 () (4). The epression is equivalent to 6 6 6 6 () () 6
More informationUnit 9: Quadratics Intercept Form
For Teacher Use Packet Score: Name: Period: Algebra 1 Unit 9: Quadratics Intercept Form Note & Homework Packet Date Topic/Assignment HW Page 9-A Graphing Parabolas in Intercept Form 9-B Solve Quadratic
More informationUnit 2 Quadratics. Mrs. Valentine Math 3
Unit 2 Quadratics Mrs. Valentine Math 3 2.1 Factoring and the Quadratic Formula Factoring ax 2 + bx + c when a = ±1 Reverse FOIL method Find factors of c that add up to b. Using the factors, write the
More informationRF2 Unit Test # 2 Review Quadratics (Chapter 6) 1. What is the degree of a quadratic function?
RF Unit Test # Review Quadratics (Chapter 6) 1. What is the degree of a quadratic function? Name: a. 1 b. c. 3 d. 0. What is the -intercept for = 3x + x 5? a. 5 b. 5 c. d. 3 3. Which set of data is correct
More informationAlgebra II: Chapter 4 Semester Review Multiple Choice: Select the letter that best answers the question. D. Vertex: ( 1, 3.5) Max. Value: 1.
Algebra II: Chapter Semester Review Name Multiple Choice: Select the letter that best answers the question. 1. Determine the vertex and axis of symmetry of the. Determine the vertex and the maximum or
More informationInstructor Quick Check: Question Block 12
Instructor Quick Check: Question Block 2 How to Administer the Quick Check: The Quick Check consists of two parts: an Instructor portion which includes solutions and a Student portion with problems for
More informationNever leave a NEGATIVE EXPONENT or a ZERO EXPONENT in an answer in simplest form!!!!!
1 ICM Unit 0 Algebra Rules Lesson 1 Rules of Exponents RULE EXAMPLE EXPLANANTION a m a n = a m+n A) x x 6 = B) x 4 y 8 x 3 yz = When multiplying with like bases, keep the base and add the exponents. a
More informationLT1: Adding and Subtracting Polynomials. *When subtracting polynomials, distribute the negative to the second parentheses. Then combine like terms.
LT1: Adding and Subtracting Polynomials *When adding polynomials, simply combine like terms. *When subtracting polynomials, distribute the negative to the second parentheses. Then combine like terms. 1.
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 informationNote: The zero function f(x) = 0 is a polynomial function. It has no degree and no leading coefficient. Sep 15 2:51 PM
2.1 Linear and Quadratic Name: Functions and Modeling Objective: Students will be able to recognize and graph linear and quadratic functions, and use these functions to model situations and solve problems.
More informationReference Material /Formulas for Pre-Calculus CP/ H Summer Packet
Reference Material /Formulas for Pre-Calculus CP/ H Summer Packet Week # 1 Order of Operations Step 1 Evaluate expressions inside grouping symbols. Order of Step 2 Evaluate all powers. Operations Step
More information