Question

Find the vertex of the parabola whose equation is y = x 2 + 8x + 12.

Answer 1

The vertex of a quadratic occurs when the velocity, dy/dx=0.

dy/dx=2x+8, so dy/dx=0 only when:

2x+8=0

2x=-8

x=-4, now you find the y coordinate which is:

y(-4)=(-4)^2+8(-4)+12

y(-4)=16-32+12

y(-4)=-4 so the vertex is at the point:

(-4,-4)

Answer 2

$y=x^2+8x+12\\\\ y=(x-p)^2+q$ W = (p,q)

$y=(x+4)^2-16+12\\\\ y=(x+4)^2-4$
W = (-4, -4)