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Polynomial Graphs
Vocabulary related to graphs of polynomial functions
Term | Definition |
---|---|
Turning Points | Where the graph changes direction |
Degree of Polynomial | The highest exponent in the polynomial |
Leading Coefficient | The number in front of the variable in the term with the highest exponent |
y-Intercept | The point where the graph crosses the y-axis |
Global Max/Min | The absolute highest or lowest point on a graph |
Local Max/Min | High and Low points that occur at turning points; Not necessarily the absolute highest and lowest point on a graph |
Zeros | The x-value that makes the function equal 0; a real zero is an x-intercept of the graph |
Multiplicity | The number of times a particular number is a zero of a polynomial |
What happens on the graph at a zero with an even multiplicity? | The graph bounces on the x-axis |
What happens on the graph at a zero with an odd multiplicity? | The graph crosses the x-axis |
End behavior of an odd degree polynomial with a positive leading coefficient | Falls left, rises right |
End behavior of an odd degree polynomial with a negative leading coefficient | Rises left, falls right |
End behavior of an even degree polynomial with a positive leading coefficient | Rises left, rises right |
End behavior of an even degree polynomial with a negative leading coefficient | Falls left, falls right |
The number of zeros of a polynomial | The number of zeros is equal to the degree of the polynomial |