Question

What is f(x) = –4x2 + 24x + 13 written in vertex form? f(x) = –4(x – 6)2 + 23 f(x) = –4(x – 6)2 + 7 f(x) = –4(x – 3)2 + 4 f(x) = –4(x – 3)2 + 49

Answer 1

We have that
f(x) = –4x² + 24x + 13

we know that

The vertex form for a parabola that opens up or down is:

f(x) = a(x - h)^2 + k

in the given equation, a=-4, therefore we add zero to the original equation in the form of 4h²−4h²
f(x) = –4x² + 24x + 4h²−4h² +13
Factor 4 out of the first 3 terms and group them 
f(x) = –4*(x² -6x +h²) +4h² +13
We can find the value of h by setting the middle term equal to -2hx
−2hx=−6x
h=3 and  4h²=36
f(x) = –4*(x² -6x +9) +36 +13

we know that the term (x² -6x +9) is equals to------> (x-3)²
so
f(x) = –4*(x-3)² +49

the answer is
f(x) = –4*(x-3)² +49