The path of a football kicked by a field goal kicker can be modeled by the equation y = –0.04x2 + 1.56x, where x is the horizontal distance in yards and y is the corresponding height in yards. what is the approximate maximum height of the football?

Our function is:
y = f(x) = -0.04x^2 + 1.56x

since we need to find maximum height and y represents that height we need to find extremum of the function. To do that all you have to do is fallowing:
1. Find first derivative of function
2. make it equal to 0 and solve for x
3. for found value of x find y in original function


1. y' = -0.08x + 1.56
2. -0.08x + 1.56 = 0
x = 1.56/0.08 = 19,5

3. y = -0.04*(19.5)^2 + 1.56 * 19.5 = 15.21

Answer is 15,21 yards