Polynomial Functions Chapter 6

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

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

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

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

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

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

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

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

Add coefficients of like terms

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

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

Evaluating Functions (Review)

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)

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

Graphing Cubic Functions

Sum/Difference of Functions Sum Difference

Modeling Situations with Sum/Difference of Functions YearF(s)M(s) 1993 (3) (6) (8) (10) (12) (15)3630

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

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

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