# What is the axis of symmetry and vertex for the graph y=x^2-10x+2?

Mar 21, 2016

vertex = (5,-23) , x = 5

#### Explanation:

The standard form of a quadratic is y$= a {x}^{2} + b x + c$

The function : $y = {x}^{2} - 10 x + 2 \text{ is in this form }$

with a = 1 , b = -10 and c = 2

the x-coord of vertex $= - \frac{b}{2 a} = - \frac{- 10}{2} = 5$

now substitute x = 5 into equation to obtain y-coord

y-coord of vertex $= {\left(5\right)}^{2} - 10 \left(5\right) + 2 = 25 - 50 + 2 = - 23$

thus vertex =( 5 , -23)

The axis of symmetry passes through the vertex and is parallel to the y-axis with equation x = 5

Here is the graph of the function with the axis of symmetry.
graph{(y-x^2+10x-2)(0.001y-x+5)=0 [-50.63, 50.6, -25.3, 25.32]}