Quadratic Polynomial
54 min 10 Examples
- Introduction to Video: Quadratic Polynomials
- Overview of Polynomial Functions and Examples #1-6 for finding the degree of polynomial
- Learning How to Identify the Important Parts of a Quadratic Polynomial
- How to Find the Axis of Symmetry, Vertex, and Number of Real Zeros of a Polynomial
- Examples #7-10: identify important parts of the polynomial function and sketch
Synthetic Division
58 min 8 Examples
- Introduction to Video: Synthetic Division
- Long Division involving Polynomials
- Overview of Synthetic Division
- Examples #1-4: Divide using Synthetic Division
- Overview of Synthetic Substitution
- The Remainder Theorem with Examples #5-6
- Examples #7-8: Use the Remainder Theorem to evaluate the polynomial
Zeros
1 hr 10 min 12 Examples
- Introduction to Video: Rational Zeros
- Understanding the Remainder Theorem, Factor Theorem, and Rational Zeros Theorem
- Examples #1-2: list all the possible rational zeros
- Fundamental Theorem of Algebra with Examples #3-4: determine the number of zeros
- Examples #5-6: One zero is given, find all others
- Example #7: One zero is given, find all others including complex roots
- Example #8: One imaginary zero is given, find all others
- Examples #9-12: Write a polynomial equation that satisfies the given conditions
Finding Zeros
57 min 10 Examples
- Introduction to Video: Finding Zeros of Polynomial Functions
- Steps for finding Zeros with Examples #1-3: list all possible zeros
- Examples #4-7: Find all rational zeros given the polynomial function
- Examples #8-9: Find all rational zeros given the polynomial function
- Example #10: Find all rational zeros, including complex, given the polynomial function
Graphing Polynomial Functions
1 hr 46 min 8 Examples
- Introduction to Video: Graphing Polynomial Functions
- Overview of Steps for Graphing Polynomial Functions
- Example #1: Graph the Polynomial Function of Degree 2
- Example #2: Graph the Polynomial Function of Degree 3
- Example #3: Graph the Polynomial Function of Degree 5
- Example #4: Graph the Polynomial Function of Degree 8
- Examples #5-6: Graph the Polynomial Function using Rational Zeros Test
- Overview of the Intermediate Value Theorem for Polynomials (Locator Theorem)
- Examples #7-8: Use the Intermediate Value Theorem for Polynomials to show a real zero exists
Polynomial Functions in Calculus
1 hr 18 min 8 Examples
- Introduction to Video: Polynomial Functions in Calculus
- Difference between open and closed intervals
- Overview of Absolute Extrema
- Overview of Local Extrema
- Example: Identify the local and absolute max and min values
- Understanding Slope of tangent lines and the Extreme Value Theorem
- Notation and Overview of Increasing and Decreasing Intervals, Critical Numbers, Maximums and Minimums, Concavity, and Inflection Points
- Examples #1-2: State whether the function has a maximum, minimum or neither
- Example: Given a graph, identify all extrema, increasing and decreasing interval, concavity, and inflection points
Chapter Test
1 hr 47 min 23 Examples
- Examples #1-2: Graph the Quadratic Polynomial
- Example #3: Graph the Quadratic Polynomial
- Examples #4-6: Find the Quotient using Synthetic Division
- Examples #7-9: Use the Remainder Theorem to Evaluate the Polynomial
- Examples #10-11: One Zero is given, find all others
- Examples #12-14: Find all Zeros and multiplicities and describe End Behavior
- Examples #15-17: Given Zeros, find a Polynomial of lowest degree
- Examples #18-19: Use the Intermediate Value Theorem for Polynomials to show a zero exists
- Example #20: Graph the Polynomial of degree 4
- Example #21: Graph the Polynomial of degree 3
- Example #22: Graph the Polynomial of degree 3
- Example #23: Graph the Polynomial of degree 6
