# How do you find the vertex and intercepts for  f(x)=-5x^2+3x+8?

Nov 17, 2015

Find vertex and intercepts of $f \left(x\right) = - 5 {x}^{2} + 3 x + 8$

#### Explanation:

x-coordinate of vertex:
$x = - \frac{b}{2 a} = - \frac{3}{-} 10 = \frac{3}{10.}$
y-coordinate of vertex:
f(3/10) = - 5(9/100) + 3(3/10) + 8 = = -45/100 + 90/100 + 800/100 = 845/100 = 8.45
To find y-intercept, make x = 0 --> y = 8
To find x-intercepts, make y = 0. Solve the quadratic equation:
$- 5 {x}^{2} + 3 x + 8 = 0.$
Since a - b + c = 0, use shortcut: the 2 real roots are:$x = - 1$ and
$x = - \frac{c}{a} = \frac{8}{5}$