1. Polynomial Functions Constant Function Linear Function Quadratic Function Cubic Function Quartic Function

2. Polynomial Functions Degree: Highest Exponent The degree determines number of possible solutions/roots/zeros PolynomialExpressionDegree Constant4 Linear-3x + 4 Quadraticx 2 + 2x – 3 Cubic2x 3 – x 2 – 2x 0 1 2 3 x0x0

3. PolynomialExpressionDegreeLeading Coefficient Constant40 Linear-3x + 41 Quadraticx 2 + 2x – 32 Cubic2x 3 – x 2 – 2x3 Polynomial Functions Leading Coefficient : coefficient on highest degree The leading coefficient determines a graph’s starting and ending behavior 4 -3 1 2

4. 1. a + 8 2. -5x 6 + 3x 3 – 8 3. 18 + 5x 2 – x 6 + 7x 8 4. (4x 2 + 3)(2x – 1) State the degree and leading coefficient of each polynomial. Degree Leading Coefficient 1 6-5 8 7 3 8

5. Polynomial Functions Even/Odd degree behavior : Even degree starts and ends in same direction. Odd degree starts and ends in opposite directions. Even Degree Even Degree Odd Degree

6. Polynomial Functions Increasing/Decreasing Patterns: Graphs are always “read” left to right. If the graph is going up, it is increasing. If the graph is going down, it is decreasing. Up Down Increasing/decreasing/increasingdecreasing/increasing/decreasing

7. A.Describe each as even or odd. B.Describe the increasing and decreasing patterns. 1.y = -x 3 + 2x 2 2. y = x 2 – 6 3. y = - 2x – 3 A:_______________ A:_______________ A:_______________ B:_______________ B:_______________ B:_______________ 4. y = x 4 + x 3 – x 2 – x – 1 5. y = -2x 2 + 4 6. y = x 3 – x 2 – 2x A:_______________ A:_______________ A:_______________ B:_______________ B:_______________ B:_______________ OddEvenOdd Even Odd dec/inc/decdecrease/increasedecrease dec/inc/dec/incincrease/decrease inc/dec/inc