# What is the vertex form of y= (x + 2)(x + 5)?

##### 1 Answer
Jun 3, 2017

Vertex form of $y = \left(x + 2\right) \left(x + 5\right)$ is $y = {\left(x + \frac{7}{2}\right)}^{2} - \frac{9}{4}$

#### Explanation:

Vertex form of equation is $y = a {\left(x - h\right)}^{2} + k$, where $\left(h , k\right)$ is the vertex.

Here we have $y = \left(x + 2\right) \left(x + 5\right)$

$= {x}^{2} + 7 x + 10$

$= {x}^{2} + 2 \times \frac{7}{2} \times x + {\left(\frac{7}{2}\right)}^{2} - \frac{49}{4} + 10$

$= {\left(x + \frac{7}{2}\right)}^{2} - \frac{9}{4}$

Hence vertex form of $y = \left(x + 2\right) \left(x + 5\right)$ is $y = {\left(x + \frac{7}{2}\right)}^{2} - \frac{9}{4}$
graph{(x+2)(x+5) [-11.75, 8.25, -4.88, 5.12]}