Solving Quadratic Equations: Completing the Square (Continued) Assignment

Complete the steps for solving 7 = -2x2 + 10x. Factor -2-125 out of the variable terms. Subtract 25/2Add 25/2Subtract 25/4Add 25/4 inside the parentheses and subtract 25/2add 25/2subtract 25/4add 25/4 on the left side of the equation. Write the perfect square trinomial as a binomial squared. Divide both sides by -2. Use the square root property of equality. Add -5/2-11/25/211/2 to both sides.

-2, add 25/4, subtract 25/2, 5/2

Solve the quadratic function by completing the square. What are the missing pieces in the steps? -32 = 2(x2 + 10x) -32 + = 2(x2 + 10x + 25) 18 = 2(x + 5)2 9 = (x + 5)2 ± = x + 5 x = -2 or x =

50, 3, -8

Complete the steps in solving the quadratic function 7x - 9 = 7x2 - 49x by completing the square. -9 = 7x2 - x -9 + = 7(x2 - 8x + )

56, 112, 16

Which are steps that could be used to solve 0 = 9(x2 + 6x) - 18 by completing the square? Check all that apply. 18 + 81 = 9(x2 + 6x + 9) 18 + 9 = 9(x2 + 6x + 9) 18 + 36 = 9(x2 + 6x + 36) 11 = (x + 3)2 = (x + 6)2 = (x + 3)2

A & D

Which are steps in the process of completing the square used to solve the equation 3 - 4x = 5x2 - 14x? Check all that apply. 3 = 5(x2 + 2x) 3 = 5x2 - 10x 4 = 5(x2 - 2x + 1) 8 = 5(x2 - 2x + 1) 3 = 5(x - 1)2 4 = 5(x - 1)2 = (x - 1)2

B, D, G

What error did Penelope make in her work? Penelope should have subtracted 1 from both sides instead of adding 1. Penelope should have subtracted 4 from both sides instead of adding 1. Penelope should have added 4 to both sides instead of adding 1. Penelope should have subtracted 8 from both sides instead of adding 1.

C. Penelope should have added 4 to both sides instead of adding 1.

What are the zeros of the quadratic function f(x) = 6x2 - 24x + 1? x = -2 + or x = -2 - x = 2 + or x = 2 - x = -2 + or x = -2 - x = 2 + or x = 2 -

D.

Andy is solving a quadratic equation using completing the square. If a step in the process results in = (x - 6)2, could the original quadratic equation be solved by factoring? Explain your reasoning.

Yes, the equation can be solved by factoring. Using the given equation, take the square root of both sides. Both 169 and 9 are perfect squares, so the left side becomes plus or minus 13/3, which is rational. Six plus 13/3 is a rational number, and 6 minus 13/3 is also a rational number. If the solutions of a quadratic equation are rational, then the equation is factorable.

5 = -6x2 + 24x 5 = -6(x2 - 4x) Add 4Add 16Subtract 4Subtract 16 inside the parentheses andadd 4 to 5 add 24 to 5 subtract 4 from 5 subtract 24 from 5 . -19 = -6(x - 2)2 = (x - 2)2 = x - 2 The two solutions are-2-1 12 .

add 4, subtract 24 from 5, 2