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?
[tex]-4*2=-8[/tex]
[tex]-4+2=-2[/tex]
So the factored form is
[tex](x-4)(x+2)[/tex]
That means the x intercepts are at [tex]x=4,-2[/tex]
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 [tex]y=a(x-h)^2+k[/tex]
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 [tex]h=\frac{-b}{2a}[/tex]
Which comes out to [tex]\frac{2}{2}[/tex] or 1.
To find the k value, we can just plug in what we got for h back into the equation.
[tex](1)^2-2(1)-8=-9[/tex]
So the vertex is [tex](1,-9)[/tex].
This also means the axis of symmetry is [tex]x=-1[/tex]
Finally, to find the y intercept, we plug in 0 for x and solve.
[tex](0)^2-2(0)-8=-8[/tex]
So the y intercept is [tex](0,-8)[/tex].
