# How do you solve  y = x^2 − 8x + 7 using the quadratic formula?

May 21, 2016

#### Answer:

The solutions for the quadratic equation are:
color(blue)(x=7
color(blue)(x=1

#### Explanation:

$y = {x}^{2} - 8 x + 7$

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 1 , b = - 8 , c = 7$

The Discriminant is given by:
$\Delta = {b}^{2} - 4 \cdot a \cdot c$

$= {\left(- 8\right)}^{2} - \left(4 \cdot 1 \cdot 7\right)$

$= 64 - 28 = 36$

The solutions are found using the formula
$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

$x = \frac{- \left(- 8\right) \pm \sqrt{36}}{2 \cdot 1} = \frac{8 \pm 6}{2}$

$x = \frac{8 + 6}{2} = \frac{14}{2} = 7$

$x = \frac{8 - 6}{2} = \frac{2}{2} = 1$