To rewrite [tex]\( y = 3x^2 + 9x - 18 \)[/tex] in the form [tex]\( y = a(x-h)^2 + k \)[/tex], the first step is to factor out the constant [tex]\(3\)[/tex] from the terms that contain [tex]\(x\)[/tex]. This will help to simplify the expression and prepare it for completing the square.
Specifically, you need to focus on the terms [tex]\( 3x^2 + 9x \)[/tex]. Factoring out the 3 from these terms gives:
[tex]\[ 3(x^2 + 3x) \][/tex]
So, the full expression [tex]\( y = 3x^2 + 9x - 18 \)[/tex] can be rewritten at this stage as:
[tex]\[ y = 3(x^2 + 3x) - 18 \][/tex]
Therefore, the correct first step is:
3 must be factored from [tex]\(3 x^2 + 9 x\)[/tex].
