Question

The height of a punted football can be modeled by the function: f(x) = -.0079 x2 + 1.8x + 1.5. In this equation, f(x) is the height in feet, and x is the horizontal distance, also in feet, from the point the ball is punted. Using that function, work through the following questions: How high is the ball when it is punted? What is the maximum height of the punt?

Answer 1

Explanation:

The function used to represent the height of a punted football can be modeled as

f(x) = -.0079x² + 1.8x + 1.5

Where f(x) is the height in feet, and x is the horizontal distance, also in feet.

a) when the ball was punted, x = 0, therefore, the height of the punted ball would be

f(x) = -.0079(0)² + 1.8(0) + 1.5

f(x) = 1.5 feet

The height is 1.5 feet

b) The equation is a quadratic equation. The plot of this equation on a graph would give a parabola whose vertex would be equal to the maximum height reached by the punted ball.

The vertex of the parabola is calculated as follows,

Vertex = -b/2a

From the equation,

a = - 0.0079

b = 1.8

Vertex = - - 1.8/0.0079 = 227.84 feet

So the maximum height of the punt is 227.84 feet