The trajectory of a rocket launched from the top of a cliff can be modeled by a quadratic equation. The rocket reaches a maximum height of 250 feet at a horizontal distance of 4 feet from the cliff. The rocket touches the ground at a horizontal distance of 9 feet from the cliff. Determine a quadratic function that models the height h(d) of the rocket at any given distance d feet from the cliff.

Question

The trajectory of a rocket launched from the top of a cliff can be modeled by a quadratic equation.  The rocket reaches a maximum height of 250 feet at a horizontal distance of 4 feet from the cliff.  The rocket touches the ground at a horizontal distance of 9 feet from the cliff.  Determine a quadratic function that models the height h(d) of the rocket at any given distance d feet from the cliff.