To find the maximum height of the arrow, we need to find the vertex of the parabolic function represented by the equation.
The vertex form of a parabolic equation is: h(t) = a(t-h)^2 + k, where (h,k) is the vertex of the parabola.
In this case, the given equation is in the form h(t) = -16t^2 + 80t + 25.
Comparing this with the vertex form, we can see that a = -16, h = -b/2a = -80/(2*(-16)) = 2.5, and k = 25.
Therefore, the time at which the arrow reaches its maximum height is 2.5 seconds. Plugging this back into the equation:
h(2.5) = -16(2.5)^2 + 80(2.5) + 25
h(2.5) = -16(6.25) + 200 + 25
h(2.5) = -100 + 200 + 25
h(2.5) = 125 feet
Therefore, the maximum height of the arrow is 125 feet.
answer this please
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 below, where "h" is the height and "t" is the time in seconds. What is the maximum height of the arrow?
`h\left(t\right)=-16t^{2}+80+25`
1 answer