# What is the vertex of y=x^2-2x+6?

Mar 17, 2016

(1 , 5 )

#### Explanation:

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

The function $y = {x}^{2} - 2 x + 6 \text{ is in this form }$

with a = 1 , b = -2 and c = 6

The x-coordinate of the vertex is found using

$x = - \frac{b}{2 a} = - \frac{- 2}{2} = 1$

substitute x = 1 into equation to obtain y-coordinate

hence: $y = {\left(1\right)}^{2} - 2 \left(1\right) + 6 = 5$

thus coordinates of vertex are ( 1 , 5 )

Here is the graph of the function.
graph{x^2-2x+6 [-20, 20, -10, 10]}