This document discusses evaluating and graphing polynomial functions. It defines a polynomial as a function with only positive or zero integer exponents. It states that a polynomial's degree refers to the highest exponent in the function. The document provides examples of linear and quadratic polynomials and their degrees. It also outlines methods for evaluating polynomials using direct substitution or synthetic substitution, and describes how to graph polynomials by determining the end behavior and making a table of values to find the middle portions.

1. Algebra 2
6.2 Evaluating and Graphing Polynomial Functions
A polynomial is a function in the form ________________________________________.
• an is called the ___________________________________________________.
• ____________ is the constant term.
• n is the _____________________ of the polynomial
A linear function, like f (x) = 3ξ + 2 is a polynomial with degree ______________.
A quadratic function, like f (x) = ξ2 + 3ξ + 2 is a polynomial with degree ____________.
Polynomials only have ___________________, _______________________ exponents.
EX1: Decide whether the function is a polynomial function. If it is, give the degree and
leading coefficient.
1
a) f (x) = ξ2 − 3ξ4 − 7 b) f (x) = ξ3 + 3ξ
2
c) f (x) = 6 ξ2 + 2 ξ−1 + ξ d) f (x) = −0.5 ξ + π ξ2 − 2
Evaluating Polynomials
EX2: Evaluate f (x) = 2 ξ4 − 8 ξ2 + 5 ξ − 7 at x = 3
“Direct Substitution”—plug and chug.
“Synthetic Substitution”
1. Write the polynomial in standard form.
• Powers of x should be in _____________________ order.
• If the polynomial is “missing” a power, put a ___________ in its place.
2. Write the __________________________ of the terms.
3. Put the number you are evaluating (in this case, 3) to the left side.
4. Bring down the ______________________ coefficient.
5. Multiply by 3 (or whatever number it is in the problem), and put it under the next
coefficient.
6. Add the column.
7. Repeat (5) and (6) until the last column is added. The answer is the last number
you write.

2. Graphing Polynomials
End Behavior: What the polynomial’s graph does at its _________________.
To graph a polynomial:
1. Figure out the ________________________________
2. Make a __________________ of values to figure out the middle.
EX 3: Graph the polynomial.
a) f (x) = ξ3 + ξ2 − 4 ξ − 1
b) f (x) = − ξ4 − 2 ξ3 + 2 ξ2 + 4 ξ
HW (evaluating) p. 333 (16 – 46 even)
HW (graphing) p. 334 (50 – 78 even)