Lesson 10.1 Solving Quadratic Equations


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1 Lesson 10.1 Solving Quadratic Equations 1. Sketch the graph of a quadratic equation with each set of conditions. a. One intercept and all nonnegative yvalues b. The verte in the third quadrant and no intercepts c. The verte in the third quadrant and two intercepts d. The verte on the yais and two intercepts, opening upward 2. Use a graph to find the number of solutions for each function. a. y 4( 3) 2 5 b. y 4( 3) 2 5 c. y ( 5) 2 d. y 3( 1) 2 1 e. y f. y g. y h. y i. y For each equation, find the solutions to the nearest hundredth by zooming in on a table or graph. a. y 2 1 b. y c. y d. y e. y 2( 5) 2 3 f. y 0.5( 3) Use a symbolic method to solve each equation. Show each solution eactly as a radical epression. a b c. 2( 1) d e f Given the two functions f() and g() , find each answer without a calculator. a. f(2) b. f(3) c. f 1 2 d. f 1 2 e. g( 2) f. g(0) g. g(2) h. g Discovering Algebra More Practice Your Skills 2002 Key Curriculum Press
2 Lesson 10.2 Finding the Roots and the Verte 1. The equation of the parabola is y ( 1)( 6). Name the  and ycoordinates of the parabola s verte. 7 y The equation of the parabola is y 1 ( 2 3)( 7). What is the line of symmetry of the parabola 13 y Find the roots of each equation, to the nearest hundredth, by looking at a graph, zooming in on a calculator table, or both. a. y b. y c. y 3( 1) 2 2 d. y e. y 2 12 f. y 6( 2) 2 4. Solve each equation symbolically and check your answer. a. 2( 1) 2 16 b. ( 5) c. 1 3 ( 5) d. ( 5) Find the solutions to 0.5( 6) 2 13, to the nearest thousandth, by graphing y 0.5( 6) 2 and y Key Curriculum Press Discovering Algebra More Practice Your Skills 67
3 Lesson 10.3 From Verte to General Form 1. Is each algebraic epression a polynomial If so, how many terms does it have If not, give a reason why it is not a polynomial. a b. 12( 5 6) c. 2 3 d. 940 e f g h i Epand each epression. a. ( 1) 2 b. ( 3) 2 c. ( 4) 2 d e. 3( 5) 2 f. 1 ( 2 2)2 3. List the first fifteen perfect square whole numbers. 4. Fill in the missing values on each rectangular diagram. Then write a squared binomial and an equivalent trinomial for each diagram. a. 3 b. 13 c d. 9 e. 0.5 f Convert each epression to general form. Check your answer by entering both epressions into the Y screen on your calculator. a. y ( 4) 2 1 b. y ( 5) 2 6 c. y ( 1) 2 1 d. y 2( 4) 2 3 e. y 4( 1) 2 2 f. y ( 3) Discovering Algebra More Practice Your Skills 2002 Key Curriculum Press
4 Lesson 10.4 Factored Form 1. Use the zero product property to solve each equation. a. ( 3)( 2) 0 b. ( 7)( 1) 0 c. 2( 2)( 2) 0 d. 1 ( 2 3)( 4) 0 e. ( 5) 0 f. ( 1)( 2)( 3) 0 g. (4 3)(3 4) 0 h. (3 6)(2 3) 0 i Graph each equation and rewrite the equation in factored form. a. y b. y c. y d. y e. y f. y Name the intercepts of the parabola of each quadratic equation. Check your answers by graphing the equations. a. y ( 7)( 1) b. y ( 2)( 6) c. y ( 8)( 8) d. y 3( 5)( 4) e. y ( 5) 2 f. y ( 0.5)( 3.5) 4. Write a quadratic equation that corresponds to each pair of roots. Assume there is no vertical shrink or stretch. Write each equation in factored form and in polynomial form. a. 3 and 1 b. 1 and 5 c. 1 2 and 1 2 d. 4 and 4 e. 1 3 and 4 f and Write quadratic equations for two different parabolas for each pair of intercepts. Write your answers in polynomial form. a. 2 and 3 b. 4 and 4 c. 2 and 5 6. Consider the equation y 3( 2)( 2). a. How many intercepts does the parabola have b. Find the verte of this parabola. c. Write the equation in verte form. Describe the transformations of the parent function, y Key Curriculum Press Discovering Algebra More Practice Your Skills 69
5 Lesson 10.6 Completing the Square 1. Solve each quadratic equation written in verte form. a b c. ( 3) d. 2( 6) e. 1 2 ( 5)2 3 0 f. 3( 4) g. 2 3 ( 6)2 3 5 h. 5( 6) i. 1.5( 5) Solve each equation written in factored form. a. ( 4)( 3) 0 b. ( 9)( 9) 0 c. ( 7)( 1) 0 d. (3 1)(3 1) 0 e. (3 5)(2 5) 0 f. ( 4)(2 1)(3 2) 0 3. Decide what number you must add to each epression to make a perfect square trinomial. Then rewrite the epression as a squared binomial. a. 2 6 b c. 2 2 d. 2 7 e f g h i. 2 (2 7 ) 4. Solve each quadratic equation by completing the square. Leave your answer in radical form. a b c d e f g h i Discovering Algebra More Practice Your Skills 2002 Key Curriculum Press
6 Lesson 10.7 The Quadratic Formula 1. Rewrite each equation in the general form a 2 b c 0 (make a 0), and name the values of a, b, and c. a b c. 3 2 d. ( 1)( 1) 0 e. ( 4) 2 3 f. (2 1)(2 3) 4 2. Without using a calculator, evaluate the epression b 2 4ac for each part in problem Use the quadratic formula to solve each equation. Give your answers in radical form and as decimals rounded to the nearest thousandth. a b c d e f g h i j k l Solve each quadratic equation. Give your answers in radical form and as decimals rounded to the nearest hundredth. a b c. ( 5) d. 2( 5) e. 1 2 ( 4)2 2 0 f. 3( 5) g. 2 3 ( 8)2 8 3 h. 5( 5) i. 2.5( 6) Key Curriculum Press Discovering Algebra More Practice Your Skills 71
7 Lesson 10.8 Cubic Functions 1. Write and solve an equation to find the value of in each figure. a. b. 7.3 cm 7.3 cm Volume 7.3 cm Volume 35,937 cm 3 2. Write the equation of the image of y 3 after the transformations. a. A slide right 2 units b. A slide up 3 units c. A slide right 2 units and up 3 units 3. Factor each epression by removing a common monomial factor. a b c d e f Factor each epression completely. a b. 3 9 c Name the intercepts of each function and write the equation in factored form. a. y b. y c. (0, 6) (0, 20) y (0, 18) ( 2, 0) (1, 0) (3, 0) ( 5, 0) ( 4, 0) ( 1, 0) ( 2, 0) (3, 0) (2, 4) 72 Discovering Algebra More Practice Your Skills 2002 Key Curriculum Press
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