# How do you find the vertex and the intercepts for y=-x^2-6x-7?

Mar 11, 2016

Vertex (-3, 2)

#### Explanation:

x-coordinate of vertex:
$x = - \frac{b}{2 a} = \frac{6}{-} 2 = - 3$
y-coordinate of vertex:
y(-3) = -9 + 18 - 7 = 2
To find y-intercept, make x = 0 --> y = -7.
To find x-intercepts, make y = 0 and solve the quadratic equation:
$y = - {x}^{2} - 6 x - 7 = 0.$
$D = {d}^{2} = {b}^{2} - 4 a c = 36 - 28 = 8$--> $d = \pm 2 \sqrt{2}$
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = \frac{6}{-} 2 \pm 2 \frac{\sqrt{2}}{-} 2 = - 3 \pm \sqrt{2}$