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Study Guides > College Algebra

Why It Matters: Power and Polynomial Functions

You’re suddenly rethinking your decision as you find yourself 456 feet above the ground on the world’s tallest roller coaster—Kingda Ka at Six Flags Great Adventure.  Perhaps, fortunately, you don’t have time to think about it because before you can catch your breath, you’re already plummeting down in a 270-degree spiral. Within your 50-second ride, you travel over 3,000 feet and reach a top speed of 128 mph. This roller coaster is not for the faint of heart! So how does a thrilling roller coaster experience come to be?  It all begins with advanced planning. Roller coaster designers use the knowledge of math, specifically polynomials, to create an experience that meets specific requirements. Photo shows a roller coaster at night with lights shining on it, tallest hill is at the forefront of the photo. Imagine you’re a roller coaster designer entrusted with the task of designing the next big attraction for a nearby theme park. Some criteria for your coaster includes a starting height of 200 ft, a dive below ground level at 3 seconds into the ride, a return to ground level at 5 seconds, and another dive beneath the ground 10 seconds later. Where do you begin?  Read on because you’ll find the answer to this question and many more in this module. At the end of the module, we’ll return to your design problem so you can come up with a plan.

Learning Objectives

Characteristics of Power and Polynomial Functions
  • Identify power functions.
  • Identify end behavior of power functions.
  • Identify polynomial functions.
  • Identify the degree and leading coefficient of polynomial functions.
  • Identify local behavior of polynomial functions.

Graphs of Polynomial Functions

  • Identify zeros of polynomial functions with even and odd multiplicity
  • Use the degree of a polynomial to determine the number of turning points of its graph
  • Draw the graph of a polynomial function using end behavior, turning points, intercepts, and the intermediate value theorem
  • Write the equation of a polynomial function given it’s graph

Divide Polynomials

  • Use long division to divide polynomials.
  • Use synthetic division to divide polynomials.

Methods for Finding Zeros of Polynomials

  • Evaluate a polynomial using the Remainder Theorem.
  • Use the Factor Theorem to solve a polynomial equation.
  • Use the Rational Zero Theorem to find rational zeros.
  • Find zeros of a polynomial function.
  • Use the Linear Factorization Theorem to find polynomials with given zeros.
  • Use Descartes’ Rule of Signs.
  • Solve real-world applications of polynomial equations

Licenses & Attributions

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  • Why It Matters: Power and Polynomial Functions. Authored by: Lumen Learning. License: CC BY: Attribution.

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