Question

Elaine shoots an arrow upward at a speed of 32 feet per second from a bridge that is

28 feet high. The height of the arrow is given by the function h(t) = -16t2 + 32t + 28,
where t is the time in seconds. What is the maximum height that the arrow reaches?

Answer 1

The height of the arrow is given by the function h(t) = -16t^2 + 32t + 28.

To find the maximum height that the arrow reaches, we need to find the vertex of the parabolic function h(t). The vertex of a parabola in the form y = ax^2 + bx + c is given by (-b/2a, c - b^2/4a).

In this case, a = -16, b = 32, and c = 28, so the vertex is located at:

t = -b/2a = -32/(2(-16)) = 1

h(1) = -16(1)^2 + 32(1) + 28 = 44

Therefore, the maximum height that the arrow reaches is 44 feet.