Solving Quadratic Equations: Completing the Square (Continued) Answers

What error did Penelope make in her work?

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 =

5 = –6x2 + 24x 5 = –6(x2 – 4x) inside the parentheses and . –19 = –6(x – 2)2 = (x – 2)2 = x – 2 The two solutions are .

add 4 to 5 add 24 to 5 subtract 4 from 5 ✔ subtract 24 from 5

–2–1 1✔ 2

Complete the steps for solving 7 = –2x2 + 10x. Factor out of the variable terms. inside the parentheses and 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 to both sides.

Subtract 25/2Add 25/2Subtract 25/4✔ Add 25/4

✔ subtract 25/2add 25/2subtract 25/4add 25/4

–5/2–11/2✔ 5/211/2

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

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 – 10x4 = 5(x2 – 2x + 1)8 = 5(x2 – 2x + 1)3 = 5(x – 1)24 = 5(x – 1)2 = (x – 1)2

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