Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Quadratic Equations And Polynomials
Introduction: Building Functions from Powers
Linear functions (f(x)=mx+b) are useful, but they describe only straight-line relationships. The real world is more complex. The path of a cannonball, the growth of a population, the shape of a suspension bridge—these require functions with higher powers.
Polynomial functions are built by adding together terms of the form anxn, where nis a non-negative integer. They form the foundation for modeling countless real-world phenomena.
What Is a Polynomial Function?
A polynomial function is a sum of terms, each consisting of a constant multiplied by a variable raised to a non-negative integer power.
f(x)=anxn+an-1xn-1+⋯+a2x2+a1x+a0
Where an,an-1,…,a0are constants (real numbers), and nis a non-negative integer.
| Term | Name | | n | Degree of the polynomial | | an | Leading coefficient | | a0 | Constant term |