Question

How do you find the vertex and the intercepts for `y = x^2 + 8x + 15`?

Answer 1

Vertex (-4, -1)

Explanation:

x-coordinate of vertex:
`x = -b/(2a) = -8/2 = -4`
y-coordinate of vertex:
y(-4) = 16 - 32 + 15 = - 1
Vertex (-4, -1)
To find y-intercept, make x = 0 --> y = 15.
To find x-intercepts, make y= 0, and solve the quadratic equation
`y = x^2 + 8x + 15 = 0`
Find 2 numbers knowing sum (-b = -8) and product (c = 15).
The 2 real roots (x-intercepts) are: - 3 and - 5.
graph{x^2 + 8x + 15 [-10, 10, -5, 5]}