Question

Jeremy stands on the edge of a river and throws a rock into the water. The rock leaves his hand at a height 4 feet above the water. The rock reaches the highest point along its path when it is a horizontal distance of 28 feet from his hand and 17 feet above the water. Write a function to represent the height of the rock in terms of its distance from Jeremy’s hand.

Answer 1

The height, h, of the rock as a function of the horizontal distance from Jeremy's hand is h = -13/784·(x - 28)² + 17

Explanation:

The given parameters are;

The height of the rock above the water when it leaves Jeremy's hand = feet

The maximum height of the rock = 28 feet

The horizontal distance at maximum height = 17 feet

Therefore, the given coordinates of the maximum height = (28, 17)

The equation of a parabola in vertex form is f(x) = a(x - h)² + k

Taking the maximum point as the vertex of the parabola, we have;

(h, k) = (28, 17)

Substituting the values gives;

f(x) = a·(x - 28)² + 17

At x = 0, the height = 4, we have;

f(0) = 4 = a·(0 - 28)² + 17

4 - 17 = a×28²

-13 = 784 × a

a = -13/784

Therefore, the height of the rock, f(x) = h, as a function of the horizontal distance from Jeremy's hand is therefore;

f(x) = h = -13/784·(x - 28)² + 17