Quadratic Equation=Find the height of the ball and the maximum of the basketball.

Question

A basketball player takes a shot. The height of the ball, h, in meters, can be modeled by the function h=-4t^2+8t+3, where t is time in seconds.

a) What is the height of the ball after 2 seconds?

b)What is the maximum height of the basketball?

c)At what time does the basketball reach its maximum height?

Answer 1

Question a) To find the height of the ball after 2 seconds, plug in t = 2:

h(2) = -4(2)² + 8(2) + 3 = 3 meters

Quest b) The maximum height occurs at the vertex of the parabola h(t) = -4t² + 8t + 3. To find the vertex, use x = -b/(2a) to find the "x-value" (actually, in this case it is the t-value) of the vertex, a = -4, b = 8, c = 3 so the -b/(2a) = -8/[(2)(-4)] = 1 so the maximum height occurs after 1 second. To find the height, plug in t = 1:

h(1) = -4(1)² + 8(1) + 3 = 7 meters

Question c) See the explanation under question b. t = 1 second