# What is the vertex of y=x^2+9x+8?

Apr 19, 2017

Vertex is $\left(- \frac{9}{2} , - \frac{49}{4}\right)$.

#### Explanation:

For finding vertex of the equation, we should convert it in the form $\left(y - k\right) = {\left(x - h\right)}^{2}$, where $\left(h , k\right)$ is the vertex.

As $y = {x}^{2} + 9 x + 8$

= x^2+2×9/2×x+(9/2)^2-(9/2)^2+8

= ${\left(x + \frac{9}{2}\right)}^{2} - \frac{81}{4} + 8$

= ${\left(x + \frac{9}{2}\right)}^{3} - \frac{49}{4}$

i.e. $y + \frac{49}{4} = {\left(x + \frac{9}{2}\right)}^{2}$

or $\left(y - \left(- \frac{49}{4}\right)\right) = {\left(x - \left(- \frac{9}{2}\right)\right)}^{2}$

Hence, vertex is $\left(- \frac{9}{2} , - \frac{49}{4}\right)$.

graph{x^2+9x+8 [-15.08, 4.92, -12.72, -2.72]}