Explanation:
To convert to vertex form, you need to complete the square. The first step is to factor out the leading coefficient from the first two terms.
f(x) = 3x² + 6x − 8
f(x) = 3 (x² + 2x) − 8
The second step is to take half of the x coefficient, square the result, then add and subtract inside the parentheses. (2/2)² = 1.
f(x) = 3 (x² + 2x + 1 − 1) − 8
Distribute:
f(x) = 3 (x² + 2x + 1) − 3(1) − 8
Factor and simplify:
f(x) = 3 (x + 1)² − 11