To rewrite the quadratic equation [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 common factor from the terms [tex]\( 3x^2 \)[/tex] and [tex]\( 9x \)[/tex].
The correct step is to factor out 3 from [tex]\( 3x^2 + 9x \)[/tex]:
[tex]\[ 3x^2 + 9x = 3(x^2 + 3x) \][/tex]
So, the first step when rewriting [tex]\( y = 3x^2 + 9x - 18 \)[/tex] in the vertex form is to factor out 3 from [tex]\( 3x^2 + 9x \)[/tex].
Thus, the correct answer is:
3 must be factored from [tex]\( 3x^2 + 9x \)[/tex].
