# 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 y-values 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 y-ais 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 y-coordinates 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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