Question 831047
Azim is the best basketball playerof all time.The height of his basketball shot from the top of his head is modeled by the function h(t)=-t^2+4t+6, h(t) us vertical displacement from his head and t is is time in seconds. Azim is 6 feet tall and standing on the ground. What is the maximum height in feet that the ball will reach from the ground?
.
h(t)=-t^2+4t+6
this is a "quadratic" (parabola) that opens downwards (from the coefficient associated with the first term).
This means the "vertex" will be at its maximum height.
The "time" at which it will reach this height is:
t = -b/(2a)
t = -4/(2*(-1))
t = -4/(-2)
t = 2 seconds
.
Height at this time, we plug it back into the original equation:
h(t)=-t^2+4t+6
h(2)=-2^2+4(2)+6
h(2)=-4+8+6
h(2)=4+6
h(2) = 10 feet (answer)