Question

What is the vertex form of `y= x^2 + 3x - 28`?

Answer 1

`y=(x-3/2)^2+(-121/4)`

Explanation:

The vertex form for a parabolic equation is:
`color(white)("XXX")y=m*(x-color(red)(a))^2+color(green)(b)`
with vertex at `(color(red)(a),color(green)(b))`

Given:
`color(white)("XXX")y=x^2+3x-28`

Complete the square:
`color(white)("XXX")y=x^2+3xcolor(blue)(+(3/2)^2) -28 color(blue)(-9/4)`

Rewrite as a squared binomial plus a (simplified) constant
`color(white)("XXX")y=1*(x-color(red)(3/2))^2+(color(green)(-121/4))`
graph{x^2+3x-28 [-41.75, 40.47, -40.33, 0.74]}