The Base Ball Question

Question

The path of a baseball thrown at a 25 degree angle to the ground can be modeled by the equation h=-0.01x^2 + 0.7x + 6, where h is the height in feet and x is the horizontal distance from the player. Find the maximum height of the baseball to the nearest tenth of a foot

Answer 1

h(x) = -0.01x² + 0.7x + 6

h(x) is a quadratic equation so its graph is a parabola. Since the leading coefficient (-0.01) is negative, the parabola is inverted with the vertex at the top. The coordinates of the vertex will then be where the ball is at its highest point: the x-coordinate will be the horizontal distance from the player and the y-coordinate will the ball's maximum height.

The x-coordinate of the vertex occurs at the point x = -b/2a. In the h(x) equation above, b = 0.7 and a = -0.01. To find the y-coordinate (height), plug the value you get for the x-coordinate into the h(x) equation. As the question states, round both answers to the nearest tenth of a foot.. The units are feet.