Recognizing Polynomial Equations from their Graphs
A polynomial equation is any equation that has an equation of the form:
y = c_{0} + c_{1}Â·x + c_{2}Â·x^{2} + ... + c_{n}Â·x^{n}
where the powers of x must be integers. The letters c_{0}, c_{1}, â€¦ , c_{n} 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 twostep
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.
Name 
Typical appearance
of graph 
Equation
(a, b, c, d, e are all
constants) 
Characteristics 
Constant equation 

y = a 
Flat, horizontal
graph 
Linear equation 

y = ax + b 
Graph is a straight
line 
Quadratic equation 

y = ax^{2} + bx + c 
One â€œhumpâ€

Cubic equation 

y = ax^{3} + bx^{2} + cx + d

May have two
â€œhumpsâ€ or an
â€œinflection pointâ€ 
Quartic equation 

y = ax^{4} + bx^{3} + cx^{2} + dx
+ e 
May have one or
three â€œhumpsâ€ or
one â€œhumpâ€ and an
â€œinflection pointâ€ 
Table 1: Equations and typical graphs for polynomial equations of order zero to four.
