To begin writing the function [tex]\( f(x) = 3x^2 + 6x - 8 \)[/tex] in vertex form, we can start by factoring out 3 from the first two terms. Here's the first step, detailed step-by-step:
1. Identify the terms for factoring out: The quadratic term [tex]\( 3x^2 \)[/tex] and the linear term [tex]\( 6x \)[/tex].
2. Factor out the greatest common factor (GCF) from these terms: The GCF of [tex]\( 3x^2 \)[/tex] and [tex]\( 6x \)[/tex] is 3.
3. Rewrite the expression with 3 factored out:
[tex]\[
f(x) = 3x^2 + 6x - 8
\][/tex]
When we factor out 3 from the terms [tex]\( 3x^2 \)[/tex] and [tex]\( 6x \)[/tex], we get:
[tex]\[
f(x) = 3(x^2 + 2x) - 8
\][/tex]
At this point, our function is:
[tex]\[
f(x) = 3(x^2 + 2x) - 8
\][/tex]
This is the first step in the process of transforming the given quadratic function into its vertex form.
