We are given this equation
[tex] y=-2x^{2} +2x+2 [/tex]
The vertex form is given by:
[tex] y=a(x-h)^{2} +k [/tex]
Now let us try to convert our equation into vertex form:
[tex] y=-2x^{2} +2x+2 [/tex]
Vertex form is given by:
[tex] y=-2(x-0.5)^{2} +2.5 [/tex]
comparing our equation with vertex form ,
The vertex (h,k) is (0.5, 2.5)
Next we have to find y when x=6, plugging x as 6 in the given equation,
[tex] y=-2(6)^{2} +2(6)+2 [/tex]
y=-58
So at x=6, y=-58.
