Why U
Algebra 86 - Graphing Polynomial Functions - Part 1
Calculators and graphing utilities are available that are capable of creating accurate graphs of polynomial functions. However, it is often desirable to sketch a quick representation of a function's graph to get a general idea of its...
Why U
Algebra 87 - Graphing Polynomial Functions - Part 2
When sketching the graph of a polynomial function, it may not be necessary to calculate numerous points on the graph. Many clues as to the general shape of the graph can be derived if we understand the characteristics that the graphs of...
Why U
Algebra 85 - Building Polynomial Functions
Because of the tremendous variety of shapes of their graphs, polynomial functions are important tools for modeling phenomena in a wide range of fields such as science, engineering, medicine and finance. But since polynomial functions are...
Brian McLogan
Graphing a fourth degree polynomial
👉 Learn how to use the tools needed to graph a Polynomial function in standard form. The tools we will use to help us graph are end behavior, finding the zeros by factoring synthetic division as well as identify the multiplicity of each...
Why U
Algebra 84 - Monomial Building Blocks of Polynomial Functions
A polynomial is a sum of one or more terms called monomials. If we think of each monomial as a separate function, then a polynomial function can be thought of as a sum of these monomial functions. In previous lectures we have studied...
Why U
Algebra 88 - Adding and Subtracting Polynomial Functions
Adding polynomial functions produces another polynomial function. The values of this function are the sum of the values of the polynomials that were added for every possible value of the input variable(s). Fortunately, adding polynomial...
Brian McLogan
Learn to determine the hypothesis and conclusion of a conditional statement
👉 Learn how to label the parts of a conditional statement. A conditional statement is an if-then statement connecting a hypothesis (p) and the conclusion (q). If the hypothesis of a statement is represented by p and the conclusion is...
Brian McLogan
Determine the multiplicity and zeros and graph of a polynomial
👉 Learn how to use the tools needed to graph a polynomial function in factored form. A polynomial in factored form is when the polynomial is written as a product of its linear factors. Each linear factor represents an x-intercept and the...
Why U
Algebra 89 - Multiplying Polynomial Functions
In the previous lecture we saw how polynomial functions could be added or subtracted, producing new polynomial functions with different characteristics. In this lecture we will see how to multiply polynomial functions and show how the...
Curated Video
Comparing Polynomial Functions: Determining Which Function Exceeds the Other
In this lesson, students will learn how to determine which of two polynomial functions eventually exceeds the other by comparing their degrees. By understanding the end behavior of polynomial functions and analyzing the leading terms,...
Brian McLogan
Algebraically Determine If the Polynomial Function is Even or Odd
👉 Learn how to determine if a function is even or odd. A function is even if the graph of the function is symmetrical about the y-axis, or a function is even if f(x) = f(-x). A function is odd if the graph of the function is symmetrical...
Brian McLogan
How do we find multiplicity and use it to graph a polynomial
👉 Learn how to use the tools needed to graph a Polynomial function in standard form. The tools we will use to help us graph are end behavior, finding the zeros by factoring synthetic division as well as identify the multiplicity of each...
Brian McLogan
Learn how to find the end behavior of a factored polynomial
👉 Learn how to determine the end behavior of the graph of a factored polynomial function. To do this we will first need to make sure we have a polynomial in standard form (i.e. we will expand all factored terms) with descending powers....
Why U
Algebra 91 - Rational Functions and Vertical Asymptotes
A rational function is any function that can be written as a fraction whose numerator and denominator are polynomials. Rational functions include a broad range of possibilities. For example, since a polynomial can be a constant, a...
Brian McLogan
Write the end behavior of a polynomial factored out
👉 Learn how to determine the end behavior of the graph of a factored polynomial function. To do this we will first need to make sure we have a polynomial in standard form (i.e. we will expand all factored terms) with descending powers....
Brian McLogan
Writing the end behavior of a polynomial using limits
👉 Learn how to determine the end behavior of the graph of a factored polynomial function. To do this we will first need to make sure we have a polynomial in standard form (i.e. we will expand all factored terms) with descending powers....
Brian McLogan
Finding the end behavior from a polynomial function
👉 Learn how to determine the end behavior of the graph of a polynomial function. To do this we will first need to make sure we have the polynomial in standard form with descending powers. We will then identify the leading terms so that...
Why U
Algebra 94 - Rational Functions with Oblique or Curvilinear Asymptotes
In the previous lecture we saw that although a rational function may have any number of vertical asymptotes or no vertical asymptotes, rational functions will always have exactly one non-vertical asymptote. Unlike vertical asymptotes, a...
Why U
Algebra 93 - Rational Functions and Nonvertical Asymptotes
Although a rational function may have any number of vertical asymptotes or no vertical asymptotes, rational functions will always have exactly one non-vertical asymptote. Since a function's value is undefined at a vertical asymptote, its...
Curated Video
Determining the End Behavior of Polynomial Functions
This video explains how to determine the end behavior of polynomial functions by identifying the degree of the function. It covers both even and odd degree polynomials, discussing how the left and right sides of the graph behave. The...
Curated Video
Finding X Intercepts of Polynomial Functions by Analyzing Factors
This video explains the concept of X intercepts and their relationship to the factors of a polynomial function. They demonstrate how to find the X intercepts graphically and algebraically by setting the function equal to zero and...
Visual Learning Systems
The Power of Moving Plates on Earth
The video discusses the power of moving tectonic plates and their impact on geological events throughout Earth's history. It showcases various examples, such as the Appalachian mountain range in Quebec, a geyser in Iceland, and...
Next Animation Studio
Explainer: What is the U.S. Electoral College and how does it work?
Americans don’t actually vote for a presidential candidate. The real power that chooses the next commander-in-chief is the Electoral College.
Curated Video
Solving a Factored Polynomial Equation Using the Zero Product Property
In this video, the teacher explains how to solve polynomial equations using the 0 product property and factoring polynomials completely. The focus is on finding the zeros or roots of the function, which are the points where the function...