To begin rewriting the quadratic equation [tex]\( y = 3x^2 + 9x - 18 \)[/tex] in the form [tex]\( y = a(x - h)^2 + k \)[/tex], which is known as vertex form, the first step is to factor 3 from the terms involving [tex]\( x \)[/tex], namely [tex]\( 3x^2 + 9x \)[/tex].
Here is a detailed, step-by-step solution:
1. Start with the original equation:
[tex]\[
y = 3x^2 + 9x - 18
\][/tex]
2. Factor out 3 from the terms [tex]\( 3x^2 \)[/tex] and [tex]\( 9x \)[/tex]:
[tex]\[
y = 3(x^2 + 3x) - 18
\][/tex]
Therefore, the first step is to factor 3 from the expression [tex]\( 3x^2 + 9x \)[/tex], and you end up with:
[tex]\[
3(x^2 + 3x) - 18
\][/tex]
Hence, the correct step is: [tex]\( \boxed{3 \text{ must be factored from } 3x^2 + 9x} \)[/tex].
