Please help! Quadratic function solving

Question

A basketball player shoots a basketball with an initial velocity of 15 ft/sec. The ball is released from an initial height of 6.5 feet.

The function         models the height, in feet, of an object after  seconds.  is the initial velocity of the object, and  is the initial height of the object.

Part 1: Write a function that models the height of the basketball. Use your function to answer Parts 2-4.

Part 2: How long does it take for the basketball to hit the ground? Round your answer to the nearest hundredth. Show all of your work.  You're welcome to use this quadratic formula calculator, but please explain your answer. (Links to an external site.)

Part 3: When does the basketball reach its maximum height? Round your answer to the nearest hundredth. Show all of your work and explain your answer.

Part 4: What is the maximum height of the basketball? Round your answer to the nearest hundredth. Show all of your work and explain your answer.

Answer 1

(1)

Plug the given initial speed and height into h(t).

h(t) = -16t² + 15t + 6.5

(2)

It hits the ground when h(t) = 0. Use the quadratic formula to solve h(t) = 0. You will get a positive and a negative value. Since time starts at t = 0, the correct solution is the positive value.

(3)

Maximum height is reached at the vertex of the height-vs.-time parabola, which occurs at

t = -b/(2a)

a = -16

b = 15

Plug in the numbers and get t.

(4)

Evaluate h(t) at the time found in part (3).