A26-2 Polynomials Notes
- 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)