Algebra Tutorials! Home Solving Quadratic Equations by Completing the Square Graphing Logarithmic Functions Division Property of Exponents Adding and Subtracting Rational Expressions With Like Denominators Rationalizing the Denominator Multiplying Special Polynomials Functions Solving Linear Systems of Equations by Elimination Solving Systems of Equation by Substitution and Elimination Polynomial Equations Solving Linear Systems of Equations by Graphing Quadratic Functions Solving Proportions Parallel and Perpendicular Lines Simplifying Square Roots Simplifying Fractions Adding and Subtracting Fractions Adding and Subtracting Fractions Solving Linear Equations Inequalities in one Variable Recognizing Polynomial Equations from their Graphs Scientific Notation Factoring a Sum or Difference of Two Cubes Solving Nonlinear Equations by Substitution Solving Systems of Linear Inequalities Arithmetics with Decimals Finding the Equation of an Inverse Function Plotting Points in the Coordinate Plane The Product of the Roots of a Quadratic Powers Solving Quadratic Equations by Completing the Square
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# 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.

 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 = ax2 + bx + c One â€œhumpâ€ Cubic equation y = ax3 + bx2 + cx + d May have two â€œhumpsâ€ or an â€œinflection pointâ€ Quartic equation y = ax4 + bx3 + cx2 + 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.