Question

The first steps in writing f(x) = 3x2 – 24x + 10 in vertex form are shown.

f(x) = 3(x2 – 8x) + 10

(-8/2)^2 = 16

What is the function written in vertex form?
A.f(x) = 3(x + 4)2 – 6
B.f(x) = 3(x + 4)2 – 38
C.f(x) = 3(x – 4)2 – 6
D.f(x) = 3(x – 4)2 – 38

Answer 1

The vertex form has the general form of:

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

We have the given equation:

f(x) = 3x^2 – 24x + 10

f(x) - 10 + 3(16) = 3(x^2 -8x + 16)
f(x) + 38 = 3(x - 4)^2
f(x) = 3 (x-4)^2 -38

Then, the correct answer is D.

Answer 2

Following the steps already shown to transform the given function into the vertex form, we have:

f(x) = 3(x2 - 8x + 16) + 10 - 3(16)
f(x) = 3(x - 4)(x - 4) + 10 - 48
f(x) = 3(x - 4)2 - 38

Therefore, the function written in vertex form is:
D.f(x) = 3(x – 4)2 – 38