Completing the Square (Continued) Answers…

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What is the first step in writing f(x) = 3x2 + 6x – 8 in vertex form?

Factor out 3 from each term.

Form a perfect square trinomial by keeping the value of the function equivalent.

Write the trinomial as a binomial squared.

Factor out 3 from the first two terms.

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x = –45✔ x = –3x = 3x = 45

x = –45

✔ x = –3

x = 3

x = 45

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Write g(x) = 4x2 + 88x in vertex form.

Answers:

Blank 1:82577

Blank 2:-484

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Question text not available

Answer:

-484

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Write p(x) = 21 + 24x + 6x2 in vertex form.

Answers:

p(x) = (x + )2 –:6

p(x) = (x + )2 –:2

p(x) = (x + )2 –:3

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✔ 241224

✔ 2

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✔ 372124

✔ 3

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Compare the graphs that Jennifer and Matt drew by completing the statements.

Answers:

Jennifer’s graph is vertically shifted from Matt’s graph.:2 units down

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✔ (–3, –45), minimum(–3, 45), maximum(3, –45), minimum(3, 45), maximum

✔ (–3, –45), minimum

(–3, 45), maximum

(3, –45), minimum

(3, 45), maximum

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What is true about the transformation that was performed? Check all that apply.

g(x) has an axis of symmetry at x = 3.

g(x) is shifted down 5 units from the graph of f(x).

g(x) is shifted right 3 units from the graph of f(x).

g(x) is shifted up 4 units from the graph of f(x).

g(x) is narrower than f(x).

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What is h(x) = –3x2 – 6x + 5 written in vertex form?

h(x) = –3(x + 1)2 + 2

h(x) = –3(x + 1)2 + 8

h(x) = –3(x – 3)2 – 4

h(x) = –3(x – 3)2 + 32

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Which functions have a maximum and are transformed to the left and down of the parent function, f(x) = x2? Check all that apply. p(x) = 14(x + 7)2 + 1q(x) = –5(x + 10)2 – 1s(x) = –(x – 1)2 + 0.5g(x) = 2x2 + 10x – 35t(x) = –2x2 – 4x – 3

p(x) = 14(x + 7)2 + 1

q(x) = –5(x + 10)2 – 1

s(x) = –(x – 1)2 + 0.5

g(x) = 2x2 + 10x – 35

t(x) = –2x2 – 4x – 3

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When Nick checked his work it did not match the standard form function. Analyze Nick’s work. What was his mistake?

In step 1, he did not put the function in standard form correctly.

In step 2, he should have also factored –7 from the constant term, 17.

In step 3, he did not subtract –7(9) to keep the function equivalent.

In step 4, he did not write the perfect square trinomial correctly as a binomial squared.

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