Important Concepts for This Unit
Functions defined by polynomial expressions are called polynomial functions. The graphs of polynomial functions can have many peaks and valleys; this makes them suitable models for many real-world situations. The standards that will be assessed in this chapter are
3.2 Can graph polynomials using intercepts, end behavior, root multiplicity, and transformations.
u3.1 - Quadratic
Functions and Models
- Graphing quadratic functions
- Obtaining the exact coordinates of the vertex
by completing the square.
- Finding roots using the quadratic formula.
Core Exercises: 2, 7, 12, 23, 30, 35, 42, 46, 53, 63
Recommended: 2, 3, 6, 7, 12, 15, 23, 25, 30, 35, 38, 42, 43, 46, 49,
52, 53, 54, 58, 63, 65, 66
u3.2 - Polynomial
Functions and their Graphs
- The terminology and notation associated with
polynomial functions.
- Characteristics of polynomial graphs:
smoothness, continuity, end behavior, and boundaries on the number of
local maxima and minima.
- Graphing polynomials using the zeros (taking
into account multiplicity) and end behavior.
Core Exercises: 1, 8, 12, 16, 29, 36, 46, 54, 61, 67, 77,
79, 84, 88
Recommended: 1, 2, 5, 8, 10, 12, 13, 16, 17, 22, 23, 29, 36, 39,
44, 46, 49, 51, 54, 57, 61, 63, 67, 71, 75, 77, 79, 81, 84, 86, 88, 90
u3.3 Dividing Polynomials
- The division algorithm for polynomials.
- Synthetic division.
- The Remainder and Factor Theorems.
Core Exercises: 2, 4, 11, 17, 26, 38, 45, 52, 54, 58, 61,
66
Recommended: 1, 2, 4, 5, 9, 11, 14, 17, 19, 24, 26, 30, 36, 38, 41,
45, 47, 51, 52, 54, 55, 58, 60, 61, 63, 66, 68, 68, 75
u3.4 Real Zeros of Polynomials
- The Rational Zeros Theorem: The rational zeros of a
polynomial function are always quotients of factors of the constant and the
leading terms.
- Factoring large polynomials using the Rational Zeros
Theorem and the quadratic formula.
- Bounding the number and size of zeros of a polynomial
function.
Core Exercises: 2, 6, 14, 17, 25, 30, 39, 58, 55, 66, 70,
79, 85, 88, 91, 102, 106, 110
Recommended: 2, 4, 6, 8, 11, 14, 15, 17, 19, 25, 26, 30, 32, 36,
39, 45, 52, 55, 57, 58, 61, 64, 66, 70, 72, 77, 79, 82, 85, 87, 88, 91, 93, 96,
100, 102, 104, 106, 107, 110
u3.6 Rational Functions
- Various kinds of asymptotes and end behavior
of functions, particularly rational functions.
- Graphing rational functions.
Core Exercises: 3, 4, 10, 13, 22, 29, 32, 37, 47, 60, 65,
76, 79, 89
Recommended: 2, 3, 4, 7, 9, 10, 13, 16, 19, 22, 25, 28, 29, 32, 34,
37, 41, 44, 47, 49, 53, 60, 62, 65, 71, 76, 77, 79, 84, 89, 91
