Question

algebra: concepts and connections - plc transformations of quadratic functions what is the first step when rewriting $y = 6x^2 + 18x + 14$ in the form $y = a(x - h)^2 + k$? $x$ must be factored from $6x^2 + 18x$; $6$ must be factored from $6x^2 + 18x$; $6$ must be factored from $6x^2 + 14$; $16$ must be factored from $18x + 14$

Explanation:

Step1: Recall vertex form rules

To rewrite $y=ax^2+bx+c$ as $y=a(x-h)^2+k$, first factor the coefficient of $x^2$ from the $x^2$ and $x$ terms only (not the constant term).

Step2: Identify target terms

For $y=6x^2+18x+14$, the $x^2$ and $x$ terms are $6x^2+18x$, and the coefficient of $x^2$ is 6.

Answer:

6 must be factored from $6x^2 + 18x$