Quadratic equations

Question

Susie dove from the high diving board at the pool. Her height above the water, h in meters, and x, in meters is the horizontal distance away from the end of the board is given by the equation: h=-x2+2x+10

What was her maximum? height above the water during the dive? How far away was she from the diving board

Answer 1

h=-x^2 +2x +10, take the derivative and set it equal to zero to solve for x at max height

h' = -2x +2 = 0

x =1 m

plug that value back into the quadratic to calculate max heght

max h = -1 + 2 + 10 = 11 meters = maximum height, when she is 1 meter from the diving board