# What is the vertex form of y= (3x+9)(x-2) ?

Mar 12, 2017

$y = 3 {\left(x + 0.5\right)}^{2} - 18.75$

#### Explanation:

First let's expand the equation:

(3x+9)(x−2) $=$ $3 {x}^{2} - 6 x + 9 x - 18$

which simplifies to:
$3 {x}^{2} + 3 x - 18$

Let's find our vertex using $x = - \frac{b}{2 a}$ where a and b are of $a {x}^{2} + b x + c$

We find the x value of our vertex to be $- 0.5$
($- \frac{3}{2 \left(3\right)}$)

Plug it into our equation and find y to be $- 18.75$
$3 {\left(- 0.5\right)}^{2} + 3 \left(- 0.5\right) - 18$

so our vertex is at $\left(- 0.5 , - 18.75\right)$

We can also check this with a graph:
graph{(3x^2+3x-18) [-10.3, 15.15, -22.4, -9.68]}

Now that we have our vertex, we can plug it into the vertex form!

$f \left(x\right) = a {\left(x - h\right)}^{2} + k$

where $h$ is our x value of the vertex, and $k$ is the y value of the vertex.

so $h = - 0.5$ and $k = - 18.75$

In the end we find:

$y = 3 {\left(x + 0.5\right)}^{2} - 18.75$