Question

find the vertex for -x2+4x+2

Answer 1

The equation of the parabola is $y=-x^2+4x+2$.

The vertex form of a quadratic equation is $y=a(x-h)^2+k$, where the vertex is (h, k), so we will write our equation is this form and then see the vetex easily.

$\displaystyle{ -x^2+4x+2=-[x^2-4x]+2=-[(x^2-4x+4)-4]+2$

$=-[(x-2)^2-4]+2=-(x-2)^2+4+2=-(x-2)^2+6$.


Now we can clearly see that the vertex is (2, 6).



Answer: (2, 6).