Enhance Your Skills in (Polynomial Functions)

Decode Polynomial Functions—Expand Your Math Knowledge—Achieve Stellar Results

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

58 min 8 Examples

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

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

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

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

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