78.7k views
5 votes
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?

User Claytog
by
7.8k points

1 Answer

4 votes

Answer:

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

User Fetchez La Vache
by
7.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.