f(x) = -2x^2 + 8x + 3
Since the number in front of x^2 is negative this means the function has a maximum value.
The to find the point where it reaches a maximum, differentiate the function.
f '(x) = -4x + 8
Stationary points when f' (x) = 0
so -4x + 8 = 0
-4x = -8
-x = -2
x = 2
Then put x = 2 into original equation to find the value of y,
y = -2 x 2^2 + 8 x 2 + 3 = 11
So the maximum value is at (2,11)