The first step when rewriting the equation [tex]$y = -4x^2 + 2x - 7$[/tex] in the form [tex]$y = a(x-h)^2 + k$[/tex] is to factor -4 from [tex]$-4x^2 + 2x$[/tex].
Here’s the detailed reasoning:
1. Identify the quadratic part of the equation: In our equation [tex]$y = -4x^2 + 2x - 7$[/tex], the quadratic expression is [tex]$-4x^2 + 2x$[/tex].
2. Factor the leading coefficient: To rewrite the equation in the vertex form, you need to complete the square. The first step in this process is to factor out the leading coefficient from the quadratic terms. In this case, the leading coefficient of [tex]$-4x^2 + 2x$[/tex] is [tex]$-4$[/tex].
So, the correct step is:
[tex]\[ -4 \text{ must be factored from } -4x^2 + 2x. \][/tex]
When you factor [tex]$-4$[/tex] from [tex]$-4x^2 + 2x$[/tex]:
[tex]\[ -4x^2 + 2x = -4(x^2 - \frac{1}{2}x). \][/tex]
This is the first step before completing the square inside the parentheses.
