Question

Transform the standard form of the following quadratic function into vertex form and into intercept form.: f(x)= - 3x^2 - 6x + 24 What is the vertex? What are the x-intercepts?

Answer 1

f(x)=-3(x+1)^2+27

Explanation:

Forst, simplify the expression by pulling out -3, but leave 24 out.

=-3(x^2+2x)+24

Then complete the square of the equatio inside the parenthesis (remember to subtract from the outside what you add to the inside times -3).

=-3(x^2+2x+1)+24+3

=-3(x+1)^2+27

The equation is now in vertex form.

from that, we now know that the vertex is (-1,27).

Set this equation equal to 0 to find the x intercepts:

0=-3(x+1)^2+27

-27=-3(x+1)^2

9=(x+1)^2

3 and -3=x+1

x=2 and -4