Bell ProblemSimplify the expression.

5.2 Evaluate and Graph Polynomial

Standards:1. Analyze situations using algebraic symbols

2. Analyze changes in quantities

Polynomial

Polynomial- a monomial or a sum of monomials Polynomial function- a function of the form

Leading coefficient- an

Degree- nConstant term- a0

Standard Form-terms are written in descending order of exponents from left to right

Common Polynomial Functions

Ex. Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.

Ex. Use direct substitution to evaluate f(x) = 2x4 – 5x3 – 4x + 8 when x = 3.

Ex. Use direct substitution to evaluate the polynomial function for the given value of x.f(x)=x4 + 2x3 + 3x2 – 7; x = -2

Ex. Use synthetic division to evaluate f(x) = 2x4 – 5x3 – 4x + 8 when x = 3

Ex. Use synthetic division to evaluate: f(x) = 5x3 + 3x2 – x + 7; x = 2

Homework

pg. 341 #4-18 even

Bell ProblemDecide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient: f(x) = 8 – x2

End Behavior of Polynomial FunctionsThe end behavior of a function’s graph is the behavior of the graph as x approaches positive infinity ____ or negative infinity ____.

Describe the degree and leading coefficient of the polynomial function whose graph is shown.

Ex. Graph f(x) = -x3 + x2 + 3x - 3

x y-3-2-10123

Ex. Graph f(x) = x4 – x3 – 4x2 + 4

x y-3-2-10123

Homework

5.2 Practice B Worksheet #2-14 even