- Identify key features like zeros, turning points, and end behavior in graphs of polynomial functions
- Find where polynomial functions equal zero using different methods, and understand what these zeros mean
- Create and explain graphs of polynomial functions, connecting how the function is written to what its graph looks like
A theme park company is designing new roller coasters and uses polynomial functions to model the tracks’ heights.
Engineers need to analyze various aspects of the tracks including zeros (ground level points), turning points, and end behavior to ensure safety and excitement. They’re currently analyzing a segment of track modeled by [latex]f(x) = -0.1(x + 2)²(x - 1)³(x - 4)[/latex], where [latex]x[/latex] is the horizontal distance in feet from the starting point and [latex]f(x)[/latex] is the height in feet.