Solving Quadratic Equations: Completing the Square (Continued) Answers
What error did Penelope make in her work?
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-8
–5/2–11/2✔ 5/211/2
add 4 to 5 add 24 to 5 subtract 4 from 5 ✔ subtract 24 from 5
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112
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16
Complete the steps in solving the quadratic function 7x – 9 = 7x2 – 49x by completing the square.
Solve the quadratic function by completing the square. What are the missing pieces in the steps?
✔ Add 4Add 16Subtract 4Subtract 16
Complete the steps for solving 7 = –2x2 + 10x.
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
Complete the steps in solving the quadratic function 7x – 9 = 7x2 – 49x by completing the square.
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?
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 original equation can be solved by factoring. Taking the square root of both sides of (x – 6)² = 169/9 gives x – 6 = ±13/3 because 169 and 9 are perfect squares. This results in rational solutions for x (x = 31/3 and x = 5/3). Since the solutions are rational numbers, the original quadratic expression is factorable.
Subtract 25/2Add 25/2Subtract 25/4✔ Add 25/4
What did you include in your response? Check all that apply.
–2–1 1✔ 2
✔ subtract 25/2add 25/2subtract 25/4add 25/4
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