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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 + c1·x + c2·x2 + ... + cn·xn

where the powers of x must be integers. The letters c0, c1, … , 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 “hump”
Cubic equation y = ax3 + bx2 + cx + d May have two “humps” or an “inflection point”
Quartic equation y = ax4 + bx3 + cx2 + dx + e May have one or three “humps” or one “hump” and an “inflection point”

Table 1: Equations and typical graphs for polynomial equations of order zero to four.

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