# What is the vertex form of y= x^2 - 7x + 10 ?

Nov 15, 2017

When given a quadratic of the form, $y = a {x}^{2} + b x + c$, the vertex form is $y = a {\left(x + \frac{b}{2 a}\right)}^{2} - {b}^{2} / \left(4 a\right) + c$

#### Explanation:

For the given equation, $y = {x}^{2} - 7 x + 10$, $a = 1$, $b = - 7$, and #c = 10.

Substitute these values into the vertex form, $y = a {\left(x + \frac{b}{2 a}\right)}^{2} - {b}^{2} / \left(4 a\right) + c$:

$y = 1 {\left(x + \frac{- 7}{2 \left(1\right)}\right)}^{2} - {\left(- 7\right)}^{2} / \left(4 \left(1\right)\right) + 10$

Simplify:

$y = 1 {\left(x - \frac{7}{2}\right)}^{2} - \frac{9}{4}$