Answer:
(-2,-36)
Step-by-step explanation:
[tex]y=(x-4)(x+8)[/tex]
1) Find the zeros of the parabola
The zero-product property states that any value, when multiplied by 0 will equal 0. Therefore, to make y=0, either (x-4)=0 OR (x+8)=0.
Therefore, x=4 and x=-8.
2) Find the x-coordinate of the vertex
To do this, we take the average of our zeros.
[tex]\frac{4+(-8)}{2} \\=\frac{-4}{2} \\=-2[/tex]
Therefore, the x-coordinate of the vertex is -2.
3) Find the y-coordinate of the vertex
Plug the x-coordinate back into the original equation
[tex]y=(-2-4)(-2+8)\\y=(-6)(6)\\y=-36[/tex]
Therefore, the y-coordinate of the vertex is -36.
Therefore, the vertex of the parabola is (-2,-36).
I hope this helps!
