Intro to Polynomials
- 2. What is a polynomial? An expression with two or more algebraic terms. Terms are separated by +/- Common Terms: Monomial An expression with exactly one algebraic term Binomial Trinomial Standard form: When a polynomial is written in descending order of exponents
- 3. Naming Polynomials Polynomials are named based on their degree and number of terms. Degree of a Monomial: The sum of the exponents of the variables in that term Degree of a Polynomial (with one variable): The highest degree of its terms (the highest exponent) Leading Coefficient: Coefficient of term with the highest degree
- 4. Naming Polynomials (cont.) Degree Name Example 0 1 2 3 4 5 6 or more…
- 5. General Shape of Polynomial Graphs Constant Linear
- 6. General Shape of Polynomial Graphs Quadratic Cubic
- 7. General Shape of Polynomial Graphs Quartic Quintic
- 8. Important Info for Polynomial Graphs x-intercept Where the graph crosses the x-axis y-intercept Where the graph crosses the y-axis If the polynomial is a function, there will only be ONE y-intercept Why?
- 9. Important Info for Polynomial Graphs Increasing A function is increasing on an interval if the y-value increases as the x-value increases AKA, as you travel from left to right, graph goes up Decreasing A function is decreasing on an interval if the y-value decreases as the x-value increases AKA, as you travel from left to right, graph goes down
- 10. Important Info for Polynomial Graphs Relative Minimum The y-value of the lowest point of a particular region of the graph Relative Maximum The y-value of the highest point of a particular region of the graph
- 11. Important Info for Polynomial Graphs Roots, Zeros, Solutions All refer to same points on the graph Same as x-intercepts Where the graph crosses the x-axis
- 12. End Behavior of a Polynomial Graph The behavior of the graph of a function f(x) as x approaches positive or negative infinity AKA, what directions will the arrows be pointing The degree and leading coefficient determine the end behavior of the polynomial Even Degree – arrows point same direction Odd Degree – arrows point different directions Positive LC – right arrow will point up Negative LC – right arrow will point down
- 13. End Behavior Chart Degree Leading Coefficent End Behavior Shortcut Notation Even Positive Even Negative Odd Positive Odd Negative