Answer:
The vertex is at (1, -108).
Step-by-step explanation:
We have the function:
![f(x)=3(x-7)(x+5)](https://tex.z-dn.net/?f=f%28x%29%3D3%28x-7%29%28x%2B5%29)
And we want to find its vertex point.
Note that this is in factored form. Hence, our roots/zeros are <em>x</em> = 7 and <em>x</em> = -5.
Since a parabola is symmetric along its vertex, the <em>x-</em>coordinate of the vertex is halfway between the two zeros. Hence:
![\displaystyle x=\frac{7+(-5)}{2}=\frac{2}{2}=1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B7%2B%28-5%29%7D%7B2%7D%3D%5Cfrac%7B2%7D%7B2%7D%3D1)
To find the <em>y-</em>coordinate, substitute this back into the function. Hence:
![f(1)=3((1)-7)((1)+5)=3(-6)(6)=-108](https://tex.z-dn.net/?f=f%281%29%3D3%28%281%29-7%29%28%281%29%2B5%29%3D3%28-6%29%286%29%3D-108)
Therefore, our vertex is at (1, -108).