Question

I need some help with graphing again.

Answer 1

To find the x intercepts, we need to put the standard form equation into factored form.

Which two numbers multiply to -8 and add to -2?

`-4*2=-8`

`-4+2=-2`

So the factored form is

`(x-4)(x+2)`

That means the x intercepts are at
`x=4,-2`

So now we have the x intercepts.

To find the vertex, we need to convert the standard form equation into vertex form.

The formula of vertex form is
`y=a(x-h)^2+k`

Since the a value in the standard form equation is 1, the a value in vertex form is also one.

The h value can be found using the formula
`h=(-b)/(2a)`

Which comes out to
`(2)/(2)` or 1.

To find the k value, we can just plug in what we got for h back into the equation.

`(1)^2-2(1)-8=-9`

So the vertex is
`(1,-9)`.

This also means the axis of symmetry is
`x=-1`

Finally, to find the y intercept, we plug in 0 for x and solve.

`(0)^2-2(0)-8=-8`

So the y intercept is
`(0,-8)`.