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 $h=\frac{-b}{2a}$

Which comes out to $\frac{2}{2}$ 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 $(0,-8)$.