The paths of some roller-coasters may be modeled by a polynomial function where t is the time, in tens of seconds, after the ride has started and h(t) is the height, in feet. Some roller coasters go underground as well as above ground.
Write an equation of a polynomial function that can be used to model a portion of a roller-coaster ride when the coaster starts 60 feet above the ground, enters an underground tunnel after 30 seconds, and then emerges from underground 20 seconds later.
Enter your answer with "h(t)=" using ^ to represent exponents and no spaces between symbols.

Question

The paths of some roller-coasters may be modeled by a polynomial function where t is the time, in tens of seconds, after the ride has started and h(t) is the height, in feet.  Some roller coasters go underground as well as above ground.
Write an equation of a polynomial function that can be used to model a portion of a roller-coaster ride when the coaster starts 60 feet above the ground, enters an underground tunnel after 30 seconds, and then emerges from underground 20 seconds later. 
Enter your answer with "h(t)=" using ^ to represent exponents and no spaces between symbols.

anonymous · Answer

So what are the conditions we have to satisfy?

h(0) = 60
h(30) = 0
h(50) = 0
Negative between 30s and 50s, positive before and after respectively.

May I suggest a quadratic?

anonymous · Answer

I still don't understand how I would come up with the equation. I'm terrible at coming up with equations...

anonymous · Answer

Consider a quadratic equation. There are a couple of different ways you can write one down, but this one will probably serve us best:
$$f(x) = (x-a)(x-b)c$$This equation has roots at x=a and x=b.

I'll make things slightly easier for you and mention that any quadratic that satisfies the first 3 conditions also satisfies the 3rd (draw some graphs if you're not certain about this).

anonymous · Answer

I'm really sorry, but I have no idea what you're talking about. I don't understand.