1. Polynomial Functions Chapter 6

2. Polynomial Functions Variable – a symbol (letter) that represents a quantity that can vary Constant – a symbol that represents a specific number/doesn’t vary Term – constant, variable or a product of a constant and one or more variables

3. More Definitions Monomial – constant, variable or a product of a constant and one or more variables raised to counting number powers (1,2,3…) Polynomial – monomial or sum of monomials

4. Polynomial Properties Polynomials are written in descending order of the powers of the variables If there are multiple variables –v–variables are put in alphabetical order –t–terms are written in descending order according to the power of the variable that comes first in the alphabet

5. Degree One variable –e–exponent of the variable –t–two or more variables

6. Degree (cont) term with no variables degree of the polynomial –l–largest degree of any nonzero term Note: it’s not necessarily the term on the left degree

7. Naming Polynomials 1 st degreeLinear polynomial 2 nd degreeQuadratic polynomial 3 rd degreeCubic polynomial

8. Coefficients –c–constant factor –l–leading coefficient coefficient of the largest degree -3 leading coefficient

9. Like Terms –constant terms or variable terms with the same variables raised to the same powers Like TermsUnlike Terms

10. Add coefficients of like terms

11. Adding/Subtracting Polynomials Note: When subtracting distribute (-) i.e. (-1) first

12. Polynomial Function –f–function expressed as f(x) = P –w–where P is a one variable polynomial Quadratic Function –f–function whose equation is in the form –w–where a ≠ 0 –N–Note: This is known as Standard Form

13. Evaluating Functions (Review)

14. Graphing Quadratic Functions parabola minimum point (lowest point) a > 0, opens up maximum point (highest point) a < 0, opens down vertex (highest or lowest point) axis of symmetry (vertical line passing through the vertex)

15. Cubic Functions an equation that can be written in the form where a ≠ 0.

16. Graphing Cubic Functions

17. Sum/Difference of Functions Sum Difference

20. Modeling Situations with Sum/Difference of Functions YearF(s)M(s) 1993 (3)2518 1996 (6)2821 1998 (8)3022 2000 (10)3127 2002 (12)3228 2005 (15)3630

21. Find (W+M)(s) Find (W+M)(25) What does this mean? –T–There will be approximately 83 students in 2015

22. Find (W – M)(s) Find (W – M)(30) What does this mean? –There will be approximately 3 more woman students than male students in 2020

23. Find (W-M)(60) Is a negative number acceptable answer? –Y–Yes Why? –S–Since we are calculating how many more women students than male, a negative number represents more male than female students