SOLUTION: The height of a soccer ball that is kicked from the ground can
be approximated by the function:
y = -16⋅x2 + 80⋅x
where y is the height of the soccer b
You can put this solution on YOUR website! The height of a soccer ball that is kicked from the ground can be approximated by the function:
y = -16x^2 + 80x
where y is the height of the soccer ball in feet x seconds after it is kicked.
.
Find the time it takes the soccer ball to reach its maximum height: seconds
Vertex of parabola is the max.
Time when it hits the max is at the "axis of symmetry":
x = -b/(2a)
x = -80/(2(-16))
x = -40/(-16)
x = 40/16
x = 2.5 seconds
.
What is the soccer ball’s maximum height: feet
plug the value of x found above back into the original equation:
y = -16x^2 + 80x
y = -16(2.5)^2 + 80(2.5)
y = 100 feet
.
Find the time it takes from the moment the soccer ball is kicked until it returns to the ground: seconds
set y to zero and solve for x:
y = -16x^2 + 80x
0 = -16x^2 + 80x
0 = -16x(x - 5)
x = {0, 5}
0 is when it was first kicked
so the answer is
x = 5 seconds
