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

Algebra ->  Rational-functions -> 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       Log On


   

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(75887) About Me  (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
------------------------------------------------
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.
----------------------------------------
f(x) = a(x-3)(x-5)(x-10)
f(0) = -150a = 200
a = -4/3
---------------
EQUATION:
f(x) = (-4/3)(x-3)(x-5)(x-10)
graph%28400%2C300%2C-5%2C15%2C-5%2C225%2C%28-4%2F3%29%28x-3%29%28x-5%29%28x-10%29%29
==============================
Cheers,
Stan H.