Question

A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by h(t) = -16t² + 88t + 50.

a) Find the vertex of h(t).
b) Explain the meaning of the vertex in the context of this problem.
c) What is the meaning of 50 on the function?
(a) The vertex of h(t) is (2.75, 116.5).
(b) The vertex represents the highest point the ball reaches, which is 116.5 meters above the ground after 2.75 seconds.
(c) 50 represents the initial height of the ball above the ground when it was launched.

Answer 1

The vertex of the function h(t) = -16t² + 88t + 50 is (2.75, 116.5), indicating the ball reaches a maximum height of 116.5 meters after 2.75 seconds. The constant term 50 represents the ball's initial height above ground.

Step-by-step explanation:

The vertex of the quadratic function h(t) = -16t² + 88t + 50 represents the highest point in the ball's trajectory, which can be found using the vertex formula. The vertex for h(t) provides both the time after launch that the ball reaches this maximum height, and the maximum height itself. In this problem, the provided vertex is (2.75, 116.5), where 2.75 seconds is the time when the ball reaches its peak, and 116.5 meters is the height of that peak above the ground. The initial height of the ball when thrown from the top of the building is the constant term in the equation, which is 50 meters in this case.