To begin rewriting the quadratic function [tex]\(f(x) = 3x^2 + 6x - 8\)[/tex] in vertex form, the first step is to factor out 3 from the first two terms. This sets up the expression in a way that makes it easier to complete the square in subsequent steps.
Here's what that looks like:
1. Factor out 3 from the first two terms:
[tex]\[ f(x) = 3(x^2 + 2x) - 8 \][/tex]
By combining the constant term [tex]\(-8\)[/tex] from the expression, we position ourselves to complete the square within the parentheses in the next steps, ultimately leading us to convert the function into vertex form.
