Solve each equation by using the Square Root Property. Round to the nearest hundredth if necessary.
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1 1. Solve each equation by using the Square Root Property. Round to the nearest hundredth if necessary LASER LIGHT SHOW The area A in square feet of a projected laser light show is given by A = 0.16d 2, where d is the distance from the laser to the screen in feet. At what distance will the projected laser light show have an area of 100 square feet? 6. Solve each equation by completing the square Write each function in vertex form. Identify the vertex. 12. y = x 2 + 6x 5 (note: the PDF has y = x2 + 3x this is incorrect. Make correction in PDF file) 13. y = 5x x Solve each equation by using the Square Root Property. Round to the nearest hundredth if necessary esolutions Manual - Powered by Cognero Page 1
2 Solve each equation by completing the square esolutions Manual - Powered by Cognero Page 2
3 Write each function in vertex form. Identify the vertex. 44. y = x x y = x 2 22x y = 2x 2 4x y = 8x 2 64x MODELING An architect s blueprints call for a dining room measuring 13 feet by 13 feet. The customer would like the dining room to be a square, but with an area of 250 square feet. How much will this add to the dimensions of the room? 49. Solve each equation. Round to the nearest hundredth if necessary FIREWORKS A firework s distance d meters from the ground is given by d = 1.5t t, where t is the number of seconds after the firework has been lit. a. How many seconds have passed since the firework was lit when the firework explodes if it explodes at the maximum height of its path? b. What is the height of the firework when it explodes? Write each function in vertex form. Identify the vertex. 54. y = x 2 3x y = x 2 4x 56. y = 3x 2 3x + 1 esolutions Manual - Powered by Cognero Page 3
4 57. MULTIPLE REPRESENTATIONS In this problem, you will use quadratics to investigate golden rectangles and the golden ratio. a. Geometric Draw square ABCD. Locate the midpoint of Construct an arc with a radius of. Label the midpoint P. Draw Extend until it intersects the arc. Label this point Q. Construct rectangle ARQD. from B clockwise past the bottom of the square. b. Algebraic Let AD = x and CQ = 1. Use completing the square to solve for x. c. Tabular Make a table of x and values for CQ = 2, 3, and 4. d. Verbal What do you notice about the x-values? Write an equation you could use to determine x for CQ = n, where n is a nonzero real number. 58. ERROR ANALYSIS Alonso and Aida are solving x 2 + 8x 20 = 0 by completing the square. Is either of them correct? Explain your reasoning. 59. CHALLENGE Solve x 2 + bx + c = 0 by completing the square. Your answer will be an expression for x in terms of b and c. esolutions Manual - Powered by Cognero Page 4
5 60. CONSTRUCT ARGUMENTS Without solving, determine how many unique solutions there are for each equation. Are they rational, real, or complex? Justify your reasoning. a. (x + 2) 2 = 16 b. (x 2) 2 = 16 c. (x 2) 2 = 16 d. 36 (x 2) 2 = 16 e. 16(x + 2) 2 = 0 f. (x + 4) 2 = (x + 6) OPEN-ENDED Write a perfect square trinomial equation in which the linear coefficient is negative and the constant term is a fraction. Then solve the equation. 62. WRITING IN MATH Explain what it means to complete the square. Describe each step. 63. The length of a rectangular field is 16 feet less than twice the width. What is the width of the field if its area is 9216 square feet? A 60 feet B 72 feet C 80 feet D 96 feet 64. What value should be added to each side of the equation to solve the following equation by completing the square? A 36 B 294 C 324 D 648 E What is the solution set for 3x 2 7x 12 = 0? 66. Solve x 2 + 8x = 4 by completing the steps below. Step 1: x 2 + 8x + = 4 + Step 2: (x + ) 2 = Step 3: x + = ± Step 4: x = ± Step 5: x = ± Solve x 2 + 6x = 1 by completing the square. 68. Solve 2x = 6x by completing the square. esolutions Manual - Powered by Cognero Page 5
6 69. MULTI-STEP Solve the equation x x + 9 = 4 following the steps. a. What number must be added to each side of the equation to create a perfect square trinomial? b. Which is the factored form of the equation? A (x + 7) 2 = 14 B (x + 7) 2 = 36 C (x + 14) 2 = 44 D (x + 14) 2 = 49 c. Which are solutions to the equation? A 13 B 6 C 1 D 6 E 1 F Which are solutions to the equation x 2 10x + 6 = 0? A B C D 71. Which equations have solutions with complex solutions? A x 2 + 8x + 20 = 0 B x 2 10x 6 = 0 Cx 2 + x 8 = 0 D x 2 6x + 16 = 0 E x 2 + 4x + 5 = 0 F x 2 12x + 22 = 0 esolutions Manual - Powered by Cognero Page 6
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