To rewrite the equation [tex]\( y = -4x^2 + 2x - 7 \)[/tex] in the vertex form [tex]\( y = a(x-h)^2 + k \)[/tex], the first step is to factor out the coefficient of [tex]\( x^2 \)[/tex] from the quadratic and linear terms.
Here's a detailed step-by-step explanation:
1. Identify the coefficient of the [tex]\( x^2 \)[/tex] term, which is [tex]\(-4\)[/tex].
2. Factor [tex]\(-4\)[/tex] out of the terms involving [tex]\( x \)[/tex], i.e., [tex]\( -4x^2 + 2x \)[/tex].
3. When you factor [tex]\(-4\)[/tex] out of these terms, you get:
[tex]\[
-4(x^2 - \frac{1}{2}x)
\][/tex]
Hence, the correct answer is to factor [tex]\(-4\)[/tex] from the terms [tex]\(-4x^2 + 2x\)[/tex].
So, the first step is:
[tex]\[ -4 \text{ must be factored from } -4x^2 + 2x. \][/tex]
