Question

TIMED HURRY PLEASE!!!!!!!! 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?

Answer 1

y=5(x+4)^2-80 is the vertex form

Answer 2

Vertex form is f(x) = 5 (x + 4 )²- 80

Explanation:

Given function is f(x) = 40x + 5x²

Re-write the function in standard form f(x) = 5x² + 40x

Factor out the first terms f(x) = 5 (x² + 8 x)

Now, form the function to perfect square trinomial,

Add and subtract '16' in function x² + 8 x to make this perfect square.

So, f(x) = 5 (x² + 8 x + 16 - 16)

f(x) = 5 (x² + 8 x + 16 )- 5 (16)

f(x) = 5 (x + 4 )²- 5 (16)

f(x) = 5 (x + 4 )²- 80

In general vertex form is f(x) = a (x - h )² + k , where (h , k) is vertex.

So, in function f(x) = 5 (x + 4 )²- 80, vertex is ( -4 , -80)

Hence, vertex form is f(x) = 5 (x + 4 )²- 80