# How do you graph the function, label the vertex, axis of symmetry, and x-intercepts. f(x)=x^2-18x+86?

Jun 16, 2015

$f \left(x\right) = {x}^{2} - 18 x + 86$

#### Explanation:

$x$ of vertex = $x$ of symmetry = $x = - \frac{b}{2 a} = \frac{18}{2} = 9$

$y$ of vertex: $y = f \left(9\right)$= 81 - 162 + 86 = 5

To find x-intercepts, make y = 0

D = ${b}^{2} - 4 a c$ = 324 - 344 = - 20 < 0.
There are no real roots (x-intercepts). The parabola open upward (a > 0). The parabola is completely above the x-axis.