Question

Mr. Trier throws a marker in the air and catches it. The height of the marker is modeled by the function h(t) = -32t² + 33t + 3, where t is measured in seconds since the marker is released and h(t) is measured in feet above the ground. At what time does the marker reach its maximum height? What is the maximum height?

Answer 1

The marker reaches its maximum height at approximately 0.515625 seconds after being thrown, reaching an approximate maximum height of 12.25 feet.

Step-by-step explanation:

The marker's maximum height is found by determining the vertex of the parabolic function h(t) = -32t² + 33t + 3. The time at which the marker reaches its maximum height can be found using the vertex formula t = -b/2a for a quadratic equation in the form ax² + bx + c. Substituting the coefficients from our function:

t = -33/(2*(-32))

t = 33/64

t ≈ 0.515625 seconds (this is the time at which the marker reaches its maximum height).

To find the maximum height, we substitute this value back into the height function:

h(0.515625) = -32*(0.515625)² + 33*(0.515625) + 3

h(0.515625) ≈ 12.25 feet (this is the approximate maximum height reached by the marker).