# What is the vertex form of y= x(x+3) ?

Dec 13, 2015

$\left(- \frac{3}{2} , - \frac{9}{4}\right)$

#### Explanation:

Distribute the $x$.

$y = {x}^{2} + 3 x$

This is in the $a {x}^{2} + b x + c$ form of a parabola where

$a = 1 , b = 3 , c = 0$

The vertex formula of a quadratic equation is

$\left(- \frac{b}{2 a} , f \left(- \frac{b}{2 a}\right)\right)$

The $x$-coordinate is

$- \frac{b}{2 a} = - \frac{3}{2 \left(1\right)} = - \frac{3}{2}$

The $y$-coordinate is

$f \left(- \frac{3}{2}\right) = - \frac{3}{2} \left(- \frac{3}{2} + 3\right) = - \frac{3}{2} \left(- \frac{3}{2} + \frac{6}{2}\right) = - \frac{9}{4}$

Thus, the vertex is $\left(- \frac{3}{2} , - \frac{9}{4}\right)$.

graph{x(x+3) [-10, 10, -5, 5]}

Indeed, the vertex is located at the point $\left(- 1.5 , - 2.25\right)$.