Answer:
36
Step-by-step explanation:
The maximum height is the y-coordinate of the vertex
given a quadratic in standard form : ax² + bx + c : a ≠ 0
then the x-coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = - x² + 20x - 64 is in standard form
with a = - 1, b = 20 and c = - 64, hence
[tex]x_{vertex}[/tex] = - [tex]\frac{20}{-2}[/tex] = 10
substitute x = 10 into the equation for y
y = - (10)² + 20(10) - 64 = 36 ← max height
