Question

The first three steps in writing f(x) = 40x + 5x2 in vertex form are shown.

Write the function in standard form. f(x) = 5x2 + 40x
Factor a out of the first two terms. f(x) = 5(x2 + 8x)
Form a perfect square trinomial. (eight-halves) squared = 16
f(x) = 5(x2 + 8x + 16) – 5(16)
What is the function written in vertex form?

A). f(x) = 5(x + 4) – 80
B). f(x) = 5(x + 8) – 80
C). f(x) = 5(x + 4)2 – 80
D). f(x) = 5(x + 8)2 – 80

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Answer 1

Answer:

Your answer is-

Step-by-step explanation:

Rewrite f(x) = 40x + 5x2 as f(x) = 5x^2 + 40x

Factor out the 5: f(x) = 5(x^2 + 8x)

Complete the square: f(x) = 5(x^2 + 8x + 16 - 16) = 5(x+4)^2 - 80 (answer)

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Answer 2

Answer:

Option (c) is correct.

Step-by-step explanation:

Given a function f(x) = 40x + 5x²

Standard form is:  f(x) = 5x² + 40

Factor a out of the first two terms :

f(x) = 5(x² + 8x)

Form a perfect square:

f(x) = 5(x² + 8x + 16 -16)

f(x) = 5(x + 4)² - 5(16)

f(x) = 5(x + 4)² - 80

Therefore, option (c) is correct.