April shoots an arrow upward at a speed of 80 feet per second from a platform 25 feet high. The pathway of the
arrow can be represented by the equation h = -16t2 + 80t + 25, where h is the height and t is the time in
seconds. What is the maximum height of the arrow?
90 feet
140 feet
125 feet
80 feet
To find the maximum height of the arrow, we need to determine the vertex of the parabolic function represented by the equation h = -16t^2 + 80t + 25.
The formula for the t-coordinate of the vertex of a parabola in the form h = at^2 + bt + c is given by t = -b/2a. In this case, a = -16 and b = 80.
So, t = -80 / (2*-16) = -80 / -32 = 2.5
Now, we can plug this back into the original equation to find the maximum height:
h = -16(2.5)^2 + 80(2.5) + 25
h = -16(6.25) + 200 + 25
h = -100 + 200 + 25
h = 125
Therefore, the maximum height of the arrow is 125 feet.