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...
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...
Why U
Algebra 92 - Rational Functions and Holes
In the previous lecture, we saw examples of x values that cause a rational function's numerator to be zero, where those x values produce x-axis intercepts in the function's graph. We also saw x values that cause denominator zeros that...
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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...
Why U
Algebra 90 - Dividing Polynomials
This lecture explains a procedure used to divide polynomials that is analogous to the procedure used to divide integers called "long division". Dividing one polynomial (the dividend) by another (the divisor) produces a quotient that may...
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...
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...
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 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 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...
Curated Video
Describing the End Behavior of Polynomial and Exponential Functions
In this lesson, students will learn how to describe the end behavior of polynomial and exponential functions. They will understand that for polynomial functions, the end behavior is determined by the leading term, while for exponential...
Brian McLogan
How to write a quadratic of it's factors using quadratic formula
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a...
Brian McLogan
How to Find All of the Zeros of a Polynomial by Factoring, Including Imaginary
👉 Learn how to find all the zeros of a polynomial. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values...
Curated Video
Comparing Polynomial and Exponential Growth: Tables and Graphs
In this lesson, we observe that as X approaches infinity, both polynomial and exponential functions approach infinity. However, through examples and graphs, we discover that exponential functions eventually surpass polynomial functions...
Brian McLogan
How to Find All of the Zeros Including Complex When Given a Polynomial
👉 Learn how to find all the zeros of a polynomial that cannot be easily factored. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros...
Brian McLogan
Learn how to determine concavity of a polynomial function
👉 Learn how to determine the concavity of a function. A function is said to be concave up (convex) if the graph of the curve is facing upwards and the function is said to be concave down (concave) if the graph is facing down. To test for...
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...
Brian McLogan
What information can you learn from the graph of a polynomial
👉 Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls...
Brian McLogan
How to classify polynomials
👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different interger exponents of the same variable. A polynomial can be classified in two ways: by the number of terms...
Brian McLogan
Determining If a 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 to write the polynomial function given three zeros
👉 Learn how to write the equation of a polynomial when given rational zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The...
Brian McLogan
Determine the end behavior of a 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....
Brian McLogan
What is the definition of standard form, degree and leading coefficient of a polynomial
👉 Learn how to find the degree and the leading coefficient of a polynomial expression. The degree of a polynomial expression is the the highest power (exponent) of the individual terms that make up the polynomial. For terms with more...