Question

A Peabody High Track star competes in the long jump. Their jump can be modeled by the equation h(x) = -0.00025 (x - 9)^2 + 4. What is their maximum height, and how long did they jump?

Answer 1

The maximum height is 4 units, and the time at which they jumped can be found by solving a quadratic equation.

Step-by-step explanation:

To find the maximum height, we need to find the vertex of the quadratic equation h(x) = -0.00025 (x - 9)^2 + 4. The equation is in vertex form, which is h(x) = a(x - h)^2 + k where (h, k) represents the vertex. In this case, the vertex is at (9,4). Therefore, the maximum height is 4 units.

To find how long they jumped, we can set h(x) = 0 and solve for x. Since the equation is in vertex form, we can find the x-coordinate of the vertex as the time at which they reached the maximum height. Set -0.00025 (x - 9)^2 + 4 = 0. Solving this equation will give us the value of x. Just remember to take into account the range of possible solutions based on the context of the problem.