Question

The equation below describes a function that models the height of a football thrown by a player. In the equation below, y represents the height of the football, in feet, and x represents the time the football is in the air, in seconds.

y=−16x2+48x+6

The maximum height reached by this football is
feet.

Answer 1

Explanation:

The maximum height reached by the football occurs at the vertex of the parabolic function given by the equation:

y = -16x^2 + 48x + 6

The x-coordinate of the vertex can be found using the formula:

x = -b / 2a

where a = -16 and b = 48 are the coefficients of the quadratic function. Substituting these values, we get:

x = -48 / 2(-16) = 1.5

So the maximum height is reached when x = 1.5 seconds.

To find the maximum height, we substitute x = 1.5 into the original equation:

y = -16(1.5)^2 + 48(1.5) + 6

y = -16(2.25) + 72 + 6

y = -36 + 78

y = 42

Therefore, the maximum height reached by the football is 42 feet.