Quadratic Functions

Question

Please show as much work as possible and not just the answer! Thanks!

Convert the quadratic function y=3x^2+6x-6 into vertex form.

Answer 1

You need to complete the square:

f(x) = 3(x² + 2x) - 6 = 3(x² + 2x +1) - 9 = 3(x+1)² - 9

Note to complete the square 1 was added inside the parentheses, i.e. 3 to the whole equation and then 3 was subtracted: -6-3=-1

This is the vertex form; the vertex is (-1,-9).