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. = 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

The right answer for the question that is being asked and shown above is that: "C.f(x) = 5(x + 4)2 – 80." 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. = 16. f(x) = 5(x2 + 8x + 16) – 5(16). The vertex form is C.f(x) = 5(x + 4)2 – 80

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frika frika · Answer 2 · 2018-08-23T07:45:53-04:00

Use the formula \((a+b)^2=a^2+2ab+b^2\) for quadratic trinomial. Then you can form from a quadratic trinomial perfect square:

\(x^2 + 8x + 16=x^2+2\cdot x\cdot 4+4^2=(x+4)^2\).

From the last given step you have that

\(f(x) = 5(x^2 + 8x + 16)-5\cdot 16\).

Since 5·16=80, you can substitute the previous expression for perfect square into function expression and get:

\(f(x)=5(x+4)^2-80\).

This means, when x=-4, f(-4)=-80 and vertex has coordinates (-4,-80).

Answer: correct choice is C.