Polynomial Functions (Degree, End Behavior, Zeros)

The degree of a polynomial is its highest exponent. The leading coefficient is the coefficient of that highest-degree term. | Polynomial | Degree | Leading coeff | Name | |---|---|---|---| | 3x + 5 | 1 | 3 | Linear | | -2x^2 + x - 1 | 2 | -2 | Quadratic | | x^3 - 4x | 3 | 1 | Cubic | | -x^4 + 2x^2 + 1 | 4 | -1 | Quartic |

End behavior describes what happens to f(x) as x to infty and x to -infty. It depends on two things: degree (odd/even) and leading coefficient (positive/negative). | Degree | Leading coeff | Left end (x to -infty) | Right end (x to infty) | |---|---|---|---| | Even | Positive | uparrow (up) | uparrow (up) | | Even | Negative | downarrow (down) | downarrow (down) | | Odd | Positive | downarrow (…