Question

A football is kicked in the air, and it’s path can be modeled by the equation f(x) = -2(x-3)2 + 56 where x is the horizontal distance, in feet, and f(x) is the height, in feet. What is the maximum height reached by the football?

Answer 1

Maximum height = 56 feet

Explanation:

The equation is in the vertex form of the quadratic equation, whose general form is:

y = a(x - h)^2 + k, where

• a determines whether the parabola opens upward or downward (positive a signifies minimum and negative a signifies minimum),
• and (h, k) is the vertex (either a minimum or maximum).

Thus, in the equation f(x) = -2(x -3)^2 + 56, (3, 56) is the equation of the vertex (in this case the maximum) and since f(x) represents the height in feet, the max height reached by the football is 56 feet.

Answer 2

The given equation for the path of the football is f(x) = -2(x-3)^2 + 56.

This is a quadratic function in the form f(x) = a(x-h)^2 + k, where a, h, and k are constants.

Comparing this equation to the standard form, we can see that a = -2, h = 3, and k = 56.

Since the coefficient of the squared term is negative, the graph of this quadratic function is a downward-facing parabola.

The maximum height reached by the football occurs at the vertex of the parabola.

The x-coordinate of the vertex is given by x = h = 3.

The y-coordinate of the vertex is given by f(h) = k = 56.

Therefore, the maximum height reached by the football is 56 feet.

Explanation: