SOLUTION: I need help writing a polynomial function that is suppost to represent a roller coaster design. It must meet these requirements: 1. starts at a height of 200 ft 2. dives below

Question 135371: I need help writing a polynomial function that is suppost to represent a roller coaster design. It must meet these requirements:
1. starts at a height of 200 ft
2. dives below the ground at t= 3 seconds
3. comes out of the ground at t = 5 seconds, then climbs to another peak and
4. dives beneath the ground agai at t = 10 seconds.
t = time.

Answer by stanbon(48558) (Show Source):
You can put this solution on YOUR website!
I need help writing a polynomial function that is suppost to represent a roller coaster design. It must meet these requirements:
1. starts at a height of 200 ft: f(0)=200
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2. dives below the ground at t= 3 seconds (3,0)
------------------------------------------------
3. comes out of the ground at t = 5 seconds, (5,0)
then climbs to another peak (x,f(x)) and
4. dives beneath the ground again at t = 10 seconds.(10,0)
t = time.
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f(x) = a(x-3)(x-5)(x-10)
f(0) = -150a = 200
a = -4/3
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EQUATION:
f(x) = (-4/3)(x-3)(x-5)(x-10)

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Cheers,
Stan H.