Answer:
![(3,29)](https://tex.z-dn.net/?f=%283%2C29%29)
Step-by-step explanation:
There is a formula that can be used to find the x-value of the vertex of the parabola. This formula is ![x=\frac{-b}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%7D%7B2a%7D)
We have the function ![g(x)=-3x^2+18x+2](https://tex.z-dn.net/?f=g%28x%29%3D-3x%5E2%2B18x%2B2)
From this function, we can find that
![a=-3\\b=18\\c=2](https://tex.z-dn.net/?f=a%3D-3%5C%5Cb%3D18%5C%5Cc%3D2)
We can plug in our know values into the formula to get
![x=\frac{-18}{2(-3)\\} \\x=\frac{-18}{-6} \\\\x=3](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-18%7D%7B2%28-3%29%5C%5C%7D%20%5C%5Cx%3D%5Cfrac%7B-18%7D%7B-6%7D%20%5C%5C%5C%5Cx%3D3)
Then we can plug in our x-value to find the y-value of the vertex
![g(3)=-3(3)^2+18(3)+2\\\\g(3)=-3(9)+54+2\\\\g(3)=-27+54+2\\\\g(3)=29](https://tex.z-dn.net/?f=g%283%29%3D-3%283%29%5E2%2B18%283%29%2B2%5C%5C%5C%5Cg%283%29%3D-3%289%29%2B54%2B2%5C%5C%5C%5Cg%283%29%3D-27%2B54%2B2%5C%5C%5C%5Cg%283%29%3D29)
This means that the vertex would be ![(3,29)](https://tex.z-dn.net/?f=%283%2C29%29)