1. 1 Algebra 2: Section 6.2 Evaluating and Graphing Polynomial Functions (Day 1)

2. 2 Polynomial Function A function is a polynomial function if… –Exponents are all whole numbers –Coefficients are all real numbers Standard Form of Polynomial Function –All terms are written in descending order of exponents from left to right

3. 3 Parts of Polynomial Function Leading coefficient –Coefficient on highest power of x Constant term –Term that has no variable (no x) Degree of the polynomial –Exponent of the highest power of x

4. 4 Classifying Polynomial Functions Classify based on highest power of x Power of x (degree) –Constant: Degree = 0:f(x) = Degree = f(x) = –Linear: Degree = 1: f(x) = Degree = f(x) = –Quadratic: Degree = 2: f(x) = Degree = f(x) = –Cubic: Degree = 3: f(x) = Degree = f(x) = –Quartic: Degree = 4: f(x) =

5. 5 Examples Decide whether the function is a polynomial function. If it is, write the function in standard form and state its degree, type, and leading coefficient.

6. 6 Examples

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8. Evaluating a Polynomial Direct substitution – putting in the value of x in place of x and solving Synthetic substitution – similar to synthetic division but the answer is just the last number of the problem. 8

9. Direct Substitution 9

10. 10 Synthetic Substitution (Synthetic Division) Gives another way to evaluate a function Also used to divide polynomials –This will be discussed in later sections The last column is the value of the function

11. 11 Examples Use synthetic division to evaluate.

12. 12 Coefficients of x written in order Missing power of x, zero coefficient! Number you are dividing by goes in front Drop 1 st number down **Multiply Across….. Add Down ANSWER!

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14. 14 Homework P.333 16 - 26 evens 28 & 30 38 - 46 evens