Question 23273: We are working with quadratic functions and their graphs. The question is: If a baseball is projected upward from ground level with an initial velocity of 64 feet per second, then its height is a function of time, given by s(t) = -16t^2 + 64t. Graph this function for 0 < or equal to t < or equal to 4. What is the maximum height reached by the ball? Answer by stanbon(60771) (Show Source):
Quadratic equation (in our case ) has the following solutons:
For these solutions to exist, the discriminant should not be a negative number.
First, we need to compute the discriminant : .
Discriminant d=4096 is greater than zero. That means that there are two solutions: .
Quadratic expression can be factored:
Again, the answer is: -0, 4.
Here's your graph:
Your quadratic has a=-16, b=64, c=0
The max or min of this quadratic is
found at t=-b/2a =64/32 = 2
Put that value of "t" into the original
equation to find the correspondins "s"