The first step in writing the function [tex]\( f(x) = 3x^2 + 6x - 8 \)[/tex] in vertex form is to factor out 3 from the first two terms. This restructuring helps in forming a perfect square trinomial more easily.
Let's break it down:
1. Start with the original function:
[tex]\[ f(x) = 3x^2 + 6x - 8 \][/tex]
2. Factor out 3 from the first two terms (involving [tex]\(x\)[/tex]):
[tex]\[ f(x) = 3(x^2 + 2x) - 8 \][/tex]
By factoring out 3, we simplify the steps needed to complete the square for the quadratic expression inside the parentheses in the next steps.
