Question

Question #b4424

Answer 1

`y=(x-4)(x+8)` has a degree of 2, and the leading coefficient is positive 1. This means the graph is a positive parabola. It has roots at `x=4` and at `x=-8`, given by the factored form of the equation.

graph{(x-4)(x+8) [-10, 10, -40, 5]}

The axis of symmetry is between the roots, so we can take the average of 4 and -8 to find the symmetry axis.

Axis of symmetry:
`x=(-8+4)/2`
`x=-2`

Vertex: plug the value in the axis of symmetry into the equation:

`y=(-2-4)(-2+8)`
`y=(-6)(6)`
`y=-36`
Vertex at `(-2,-36)`