Question

A circus acrobat jumps off a raised platform. He lands on a trampoline at stage level below. His path can be modeled by the relation h=-0.5d^2+0.5d+6, where h is his height above the stage and d is his horizontal distance from the edge of the platform, both in meters.

a) What is the height of his platform?

Answer 1

The height of the platform can be determined by solving the quadratic equation.

Step-by-step explanation:

The height of the platform can be determined by setting h=0 and solving for d in the given equation.

0=-0.5d^2+0.5d+6

Using the quadratic formula, we can find the value of d.

1. Plug in the values a=-0.5, b=0.5, and c=6 into the quadratic formula: d = (-b ± √(b^2 - 4ac))/2a
2. Solve for d: d = (-0.5 ± √(0.25 - 4(-0.5)(6)))/2(-0.5)
3. Simplify and calculate the two possible values of d.
4. The larger value of d represents the distance from the edge of the platform to the landing position on the trampoline, so the height of the platform would be 6 meters plus this distance.

Thus, by solving the quadratic equation, we can find the height of the platform.