To begin the process of converting the quadratic function [tex]\( f(x) = 3x^2 + 6x - 8 \)[/tex] into vertex form, the first step is:
Factor out 3 from the first two terms.
Here's how you can do it step-by-step:
1. Factor out 3 from the first two terms:
The quadratic term [tex]\( 3x^2 \)[/tex] and the linear term [tex]\( 6x \)[/tex] share a common factor of 3. So, you can factor 3 out from these two terms.
[tex]\[
f(x) = 3(x^2 + 2x) - 8
\][/tex]
This step sets up the expression to more easily complete the square in the next steps, ultimately converting it into vertex form [tex]\( a(x - h)^2 + k \)[/tex].
