h(t)=-16t^2+80t

Question

h=height

t=time in seconds

have to create a graph and answer the question: how long is the golf ball in the air? relate your answer to the domain of the problem situation modeled by the function

Answer 1

Hi, Maddie,

You can solve for elapsed time in a few different ways. But let's pick the easiest.

This, as you know is a downward opening parabola. Since there is no C term, that means that the y-intercept is zero (0,0), which makes the problem somewhat easier. Since t is the elapsed time, the second (non-zero) x-intercept is the value we need. The easiest way to go about this is to find the x value of the vertex, which is found by the formula -b/2a. In this case, that's -80/-32 = 2.5.

If the ball reaches the vertex at 2.5 seconds, and the parabola (like all parabolas) is symmetrical, then, in another 2.5 seconds, it will hit the ground, at t = 5.

In discussing the domain of a real-world situation, just keep in mind that negative time and negative height don't make sense, so you have to limit the domain to [0,5] .

Best wishes!