# Question #5fd61

Feb 6, 2017

y-intercept = 8
x-intercepts:
$x = \frac{7 \pm \sqrt{17}}{2}$

#### Explanation:

$f \left(x\right) = {x}^{2} - 7 x + 8$
To find y-intercept, make x = 0
x = 0 --> y-intercept --> f(0) = 8
To find x-intercepts, make y = 0, and solve this quadratic equation by using the improved quadratic formula (Socratic Search):
${x}^{2} - 7 x + 8 = 0$
$D = {d}^{2} = {b}^{2} - 4 a c = 49 - 32 = 17$ --> $d = \pm \sqrt{17}$
There are 2 real roots (two x- intercepts):
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = \frac{7}{2} \pm \frac{\sqrt{17}}{2} = \frac{7 \pm \sqrt{17}}{2}$