Question

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

Answer 1

Vertex (-3, 2)

Explanation:

x-coordinate of vertex:
`x = -b/(2a) = 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 - 6x - 7 = 0.`
`D = d^2 = b^2 - 4ac = 36 - 28 = 8`--> `d = +- 2sqrt2`
`x = -b/(2a) +- d/(2a) = 6/-2 +- 2sqrt2/-2 = -3 +- sqrt2`