The drop that riders experience on Dr. Doom's Free Fall can be modeled by the quadratic function, h(t)9.8t2 5t 39 where h is height in meters and t is time in seconds. From what height are the riders dropped? What is the height of the riders after 1.5 seconds?

The function given is a parabola and we would expect that at the start, the riders were at the top of the ride. So at time t=0 the riders are up high (whatever the height is) and then after a certain amount of time they would go back down to the ground. The ground is a height of 0. So h(t) = 0 for t = the time it takes for the ride to end and the riders to hit the ground.

A parabola looks like the letter U but since the riders start up top, we would expect the parabola to be concave down (like an upside down U) and this would mean that the leading coefficient is negative.

The way you wrote the function there are no signs between the terms, so I am going to assume it should be [tex]h(t)=-9.8 t^{2} +5t+39[/tex]. If this is not the equation you have, you can still follow the process below to arrive at the answers you are asked for.

From what height are the riders dropped? I assume the riders are at the height (top) at the start of the ride so t = 0. To find the height we evaluate the function at t = 0 as follows: [tex]h(0)=-9.8 t^{0} +5(0)+39 = 39[/tex]. That is they are dropped from a height of 39 meters.

What is the height of the riders after 1.5 seconds?
Here t = 1.5 so we evaluate the function at t = 1.5 as follows:
[tex]h(t)=-9.8 (1.5)^{2} +5(1.5)+39[/tex]
[tex]h(1.5)=(-9.8)(2.25)+7.5+39=(-22.05)+7.5+39=24.45[/tex]
That is, after 1.5 seconds the riders are 24.45 meters off the ground.