Question

At a family picnic, you decide to have a competition with your uncle to see who can throw the football the farthest. You toss the football 60 feet and its maximum height is 25 feet. Write a quadratic

equation representing the flight of the football.

Answer 1

To represent the flight of the football, we can write a quadratic equation separately for the vertical and horizontal components. The vertical equation involves the maximum height of the ball, while the horizontal equation involves the distance traveled. The quadratic equation can be written as 25 = a(60 - p)^2 + k for the vertical component and 60 = v*t for the horizontal component.

Step-by-step explanation:

To write a quadratic equation representing the flight of the football, we need to consider the vertical and horizontal components separately. Let's start with the vertical component. The maximum height of the football is 25 feet, which means that at its highest point, the vertical displacement is 25 feet. Since the motion of the football follows a parabolic path, we can use the equation h = a(x - p)^2 + k, where h represents the height, x represents the horizontal distance, p represents the horizontal position at the maximum height, and k represents the maximum height. Plugging in the values, we get 25 = a(60 - p)^2 + k. Now, let's consider the horizontal component. The horizontal distance traveled by the football is 60 feet. Since the horizontal motion is uniform, we can use the equation x = v*t, where x represents the horizontal distance, v represents the horizontal velocity, and t represents the time. Plugging in the values, we get 60 = v*t.

So, the quadratic equation representing the flight of the football is:

25 = a(60 - p)^2 + k

60 = v*t