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

Jan 28, 2016

$y = {\left(x - \frac{3}{2}\right)}^{2} + \left(- \frac{121}{4}\right)$

#### Explanation:

The vertex form for a parabolic equation is:
$\textcolor{w h i t e}{\text{XXX}} y = m \cdot {\left(x - \textcolor{red}{a}\right)}^{2} + \textcolor{g r e e n}{b}$
with vertex at $\left(\textcolor{red}{a} , \textcolor{g r e e n}{b}\right)$

Given:
$\textcolor{w h i t e}{\text{XXX}} y = {x}^{2} + 3 x - 28$

Complete the square:
$\textcolor{w h i t e}{\text{XXX}} y = {x}^{2} + 3 x \textcolor{b l u e}{+ {\left(\frac{3}{2}\right)}^{2}} - 28 \textcolor{b l u e}{- \frac{9}{4}}$

Rewrite as a squared binomial plus a (simplified) constant
$\textcolor{w h i t e}{\text{XXX}} y = 1 \cdot {\left(x - \textcolor{red}{\frac{3}{2}}\right)}^{2} + \left(\textcolor{g r e e n}{- \frac{121}{4}}\right)$
graph{x^2+3x-28 [-41.75, 40.47, -40.33, 0.74]}