The equation of the parabola is [tex]y=-x^2+4x+2[/tex].
The vertex form of a quadratic equation is [tex]y=a(x-h)^2+k[/tex], where the vertex is (h, k), so we will write our equation is this form and then see the vetex easily.
[tex]\displaystyle{ -x^2+4x+2=-[x^2-4x]+2=-[(x^2-4x+4)-4]+2[/tex]
[tex]=-[(x-2)^2-4]+2=-(x-2)^2+4+2=-(x-2)^2+6[/tex].
Now we can clearly see that the vertex is (2, 6).
Answer: (2, 6).
