Completing the Square

Question 1

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

Revolt · Accepted Answer

Factor out 3 from the first two terms.

Question 2

Question 3

Revolt · Accepted Answer

3

Question 3

Write g(x) = 4x2 + 88x in vertex form. The function written in vertex form is g(x) = ⇒ 4 (x +11)2 + ⇒ -484.

Revolt · Accepted Answer

⇒ 4: 4(x + 11)^2 - 484; ⇒ -484: 4(x + 11)^2 - 484

Question 4

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

Revolt · Accepted Answer

(–3, –45), minimum

Question 5

Write p(x) = 21 + 24x + 6x2 in vertex form. p(x) = (x + )2 –

Revolt · Accepted Answer

6; Selection 1: 6; Selection 2: 2; Selection 3: 3

Question 6

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

Revolt · Accepted Answer

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

Question 7

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

Revolt · Accepted Answer

h(x) = –3(x + 1)2 + 8

Question 8

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

Revolt · Accepted Answer

q(x) = –5(x + 10)2 – 1; t(x) = –2x2 – 4x – 3

Question 9

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

Revolt · Accepted Answer

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

Question 10

Compare the graphs that Jennifer and Matt drew by completing the statements. Jennifer’s graph is vertically shifted from Matt’s graph. Jennifer’s graph is horizontally shifted from Matt’s graph. Jennifer’s graph is Matt’s graph. Which graph has a vertex that is a maximum?

Revolt · Accepted Answer

Selection 1: 2 units down; Selection 2: 0 units left or right; Selection 3: the same shape as; Selection 4: Neither Jennifer’s nor Matt’s

Completing the Square Answers

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