Question

what is the first step when rewriting $y = 3x^2 + 9x - 18$ in the form $y = a(x - h)^2 + k$?
9 must be factored from
$9x - 18$
3 must be factored from
$3x^2 + 9x$
3 must be factored from
$3x^2 - 18$
$x$ must be factored from
$3x^2 + 9x$

Explanation:

Step1: Recall vertex form conversion

To rewrite $y=ax^2+bx+c$ to $y=a(x-h)^2+k$, first factor the coefficient of $x^2$ from the $x^2$ and $x$ terms.

Step2: Identify target terms

For $y=3x^2+9x-18$, the $x^2$ and $x$ terms are $3x^2+9x$. Factor out 3: $3(x^2+3x)-18$.

Step3: Match to options

This matches the action of factoring 3 from $3x^2+9x$.

Answer:

3 must be factored from $3x^2 + 9x$