Recognizing Polynomial Equations from their Graphs
A polynomial equation is any equation that has an equation of the form:
y = c0 + c1Â·x + c2Â·x2 + ... + cnÂ·xn
where the powers of x must be integers. The letters c0, c1, â€¦ , cn represent numbers.
The largest power of x in the polynomial is called the degree of the polynomial.
Finding a Formula for a Polynomial Equation
Finding a formula for a polynomial equation using regression on a calculator is a two-step
process. The first step consists of deciding which type of regression to use, and the
second step consists of actually carrying out the regression on a graphing calculator to
find the formula.
Recognizing a Polynomial from its Graph
Each of the different types of polynomial equations has a distinctively shaped graph.
(a, b, c, d, e are all
|y = a
|y = ax + b
|Graph is a straight
|y = ax2 + bx + c
|y = ax3 + bx2 + cx + d
|May have two
â€œhumpsâ€ or an
|y = ax4 + bx3 + cx2 + dx
|May have one or
three â€œhumpsâ€ or
one â€œhumpâ€ and an
Table 1: Equations and typical graphs for polynomial equations of order zero to four.