Question

How do you graph the quadratic function and identify the vertex and axis of symmetry and x intercepts for `y=-(x+3)(x+5)`?

Answer 1

x-intercepts: `x=-5 and x=-3`
Axis of Symmetry: `x=-4`
Vertex: `(-4,1)`

Explanation:

x-intercepts:
Use the Null Factor Law
`x+3=0`
`x=-3`
and
`x+5=0`
`x=-5`

Axis of Symmetry:
Halfway between the two x-intercepts.
`x=(-3+(-5))/2=-4`

Vertex:
The function evaluated at the axis of symmetry
`f(-4)=-(-4+3)(-4+5)=1`
Vertex: `(-4,1)`