Putting It Together: Power and Polynomial Functions
At the start of this module, you were given the challenge of designing a roller coaster given a set of criteria. Now that you know a bit about polynomials, let’s take another look at the coaster in terms of a polynomial as a function of time, [latex]t[/latex].- The starting height of the coaster must be 200 ft, so [latex]f(0)=200[/latex].
- At [latex]t=3[/latex], the roller coaster goes below ground level, (3, 0).
- At [latex]t=5[/latex], the roller coaster returns to ground level, (5, 0).
- At [latex]t=10[/latex], the roller coaster goes below ground level again, (10, 0).
[latex]f\left(t\right)=a\left(t-3\right)\left(t-5\right)\left(t-10\right)[/latex]
[latex]f\left(t\right)=a\left(t3-18t^2+95t-150\right)[/latex]
[latex]f\left(0\right)=-150a-200[/latex]
[latex]a=-4/3[/latex]
[latex]f(t)=-4/3(t3-18t^2+95t-150)[/latex]
Graphing this polynomial will help you analyze the design better. One way to graph a polynomial function is to first find the intercepts. Earlier you found the intercepts [latex](0, 200), (3, 0), (5, 0)[/latex], and [latex](10, 0)[/latex].

Licenses & Attributions
CC licensed content, Original
- Putting It Together: Power and Polynomial Functions. Authored by: Lumen Learning. License: CC BY: Attribution.
- Polynomial Graph. Authored by: Christine Caputo for Lumen. License: CC BY: Attribution.
- Polynomial Graph with Roller Coaster. Authored by: Lumen. License: CC BY: Attribution.