Question

the height of a football in the air t seconds after it is thrown can be modeled by the function y=-16t^2+96t+3, where y are measured in feet and t is time. What is the maximum height that the football reaches? How long did it take the football to reach the maximum height? At what times will the football be above the ground at 122 feet?

Answer 1

Since the function is a parabola, the maximum height would be the y-coordinate of the vertex. The x-coordinate of the vertex in standard parabolic form is
x = -b/2a.
In the problem, t would now be x.
t = -96/(2*-16) = 3*

Now that you have the time as 3 at the vertex, you can determine the height y at the vertex by substituting it in.
y = -16(3)^2 + 96(3) + 3
y = 147*

If they give you 122 feet and you need to find the time, then just plug that as y and solve for t.
122 = -16t^2 + 96t + 3
0 = -16t^2 + 96t - 119
t = 17/4, 7/4*

*Brainliest answer is always appreciated