# What is the vertex form of y= x^2 - 9x+36?

Mar 28, 2018

Vertex form of equation is $y = {\left(x - 4.5\right)}^{2} + 15.75$

#### Explanation:

$y = {x}^{2} - 9 x + 36 \mathmr{and} y = \left({x}^{2} - 9 x + {4.5}^{2}\right) - {4.5}^{2} + 36$ or

$y = {\left(x - 4.5\right)}^{2} - 20.25 + 36 \mathmr{and} y = {\left(x - 4.5\right)}^{2} + 15.75$

Comparing with vertex form of equation

y = a(x-h)^2+k ; (h,k) being vertex we find here

$h = 4.5 , k = 15.75 , a = 1 \therefore$ Vertex is at $\left(4.5 , 15.75\right)$ and vertex

form of equation is $y = {\left(x - 4.5\right)}^{2} + 15.75$ [Ans]