what is the maximum height the ball can reach? How long will it take to reach the maximum height?

Question

A ball is thrown from a point above the ground. The height at ground level is given by the equation h=-3t^2+24t, where h is the height in meters and t is the time in seconds. What is the maximum height the ball can reach? How long will it take to reach the maximum height?

Answer 1

Notice that h = -3t^2+24t is a parabolic function with the vertex being the greatest value possible. To find the x-coordinate of the parabola, use the equation -b/2a where a = -3, b = 24, and c = 0 (f(x) = ax^2+bx+c). This will give you t = 4. To find the y-coordinate, plug in t = 4 into the equation given. The y-coordinate is the max height reached and the x-coordinate is the time it takes to reach the max height. NOTE: do not find the zeroes of the function to figure out the vertex.