Question

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

f(x) = 3(x2 – 8x) + 10

(StartFraction negative 8 Over 2 EndFraction) squared = 16

What is the function written in vertex form?

Answer 1

To write the function f(x) = 3x^2 – 24x + 10 in vertex form, we need to complete the square.

Let's start with the given expression: f(x) = 3(x^2 – 8x) + 10.

To complete the square for the quadratic expression inside the parentheses, we need to take half of the coefficient of x (-8) and square it:

(-8/2)^2 = 16.

Now we can rewrite the expression by adding and subtracting 16 within the parentheses:

f(x) = 3(x^2 – 8x + 16 - 16) + 10.

Next, we can factor the expression inside the parentheses as a perfect square:

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

Simplifying further:

f(x) = 3(x - 4)^2 - 48 + 10.

Combining like terms:

f(x) = 3(x - 4)^2 - 38.

Therefore, the function f(x) = 3x^2 – 24x + 10 in vertex form is f(x) = 3(x - 4)^2 - 38.