Polynomial functions | Elementary algebra
In algebra, a quartic function is a function of the form where a is nonzero,which is defined by a polynomial of degree four, called a quartic polynomial. A quartic equation, or equation of the fourth degree, is an equation that equates a quartic polynomial to zero, of the form where a ≠ 0.The derivative of a quartic function is a cubic function. Sometimes the term biquadratic is used instead of quartic, but, usually, biquadratic function refers to a quadratic function of a square (or, equivalently, to the function defined by a quartic polynomial without terms of odd degree), having the form Since a quartic function is defined by a polynomial of even degree, it has the same infinite limit when the argument goes to positive or negative infinity. If a is positive, then the function increases to positive infinity at both ends; and thus the function has a global minimum. Likewise, if a is negative, it decreases to negative infinity and has a global maximum. In both cases it may or may not have another local maximum and another local minimum. The degree four (quartic case) is the highest degree such that every polynomial equation can be solved by radicals, according to the Abel–Ruffini theorem. (Wikipedia).
Trigonometry: Sine, Cosine and Tangent
This video introduces the three basic trigonometric functions from the point of view of solving problems that involve triangles. The sine, cosine and tangent functions are defined, related to cosecant, secant and cotangent, and connected to the unit circle. Graphs of all of the functions a
From playlist Trigonometry
Trigonometric Functions: Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent
Oh man, what is all this sine and cosine business? What do these things even mean?! And Greek letters now? I don't know Greek! OK friend, just relax. Understanding the trig functions is as easy as pi radians. We just make some triangles and set up a few definitions. I promise it's no sweat
From playlist Trigonometry
Trigonometry - Vocabulary of trigonometric functions
In this video will cover some of the basic vocabulary that you'll hear when working with trigonometric functions. Specifically we'll cover what is trigonometry, angles, and defining the trigonometric functions as ratios of sides. You'll hear these terms again as we dig deeper into the st
From playlist Trigonometry
What is the definition of the inverse cosine function
👉 Learn how to evaluate inverse trigonometric functions. The inverse trigonometric functions are used to obtain theta, the angle which yielded the trigonometric function value. It is usually helpful to use the calculator to calculate the inverse trigonometric functions, especially for non-
From playlist Evaluate Inverse Trigonometric Functions
Introduction to Right Triangle Trigonometry (Precalculus - Trigonometry 30)
What Sine, Cosine, Tangent and the reciprocal functions refer to in a Right Triangle and how to use them. Also discussed is the Co-Function relationships and the identities that come from them. Support: https://www.patreon.com/ProfessorLeonard
From playlist Precalculus - College Algebra/Trigonometry
Trigonometric Functions and the Unit Circle (Precalculus - Trigonometry 6)
The creation of the Unit Circle and how it relates to Right Triangle Trigonometry and the creation of Trigonometric Functions. Support: https://www.patreon.com/ProfessorLeonard
From playlist Precalculus - College Algebra/Trigonometry
How to use reference angles to help evaluate for an angle
👉 Learn how to evaluate the six trigonometric functions of a given angle. When given an angle we locate the angle on the unit circle. Then using the coordinate of the terminal side of the angle on the unit circle and the definitions of the six trigonometric functions, we can then evaluate
From playlist Evaluate the Six Trigonometric Functions Given and Angle
Introduction to Hyperbolic Functions
This video provides a basic overview of hyperbolic function. The lesson defines the hyperbolic functions, shows the graphs of the hyperbolic functions, and gives the properties of hyperbolic functions. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Differentiation of Hyperbolic Functions
The Three/Four bridge and solving quartic equations | Six 7 | Wild Egg
Solving polynomial equations, or equivalently finding factorizations into linear factors, is a major theme in algebra. Here we show how the general quartic equation can be so factored if we have a prior technology for solving quadratic and cubic equations. The key idea goes back to Lagra
From playlist Six: An elementary course in Pure Mathematics
Can Mathematica Solve Polynomial Equations?
𝙒𝘼𝙉𝙏 𝙈𝙊𝙍𝙀? https://snu.socratica.com/mathematica-essentials You may have memorized the formula to solve quadratic equations. You may have seen the formula for cubic equations, or even quartic equations (although most people don't memorize these). But what about polynomial equations of hig
From playlist Mathematica & the Wolfram Language
Counting Low Degree Number Fields with Almost Prescribed Successive Minima - Sameera Vemulapalli
Joint IAS/PU Number Theory Seminar Topic: Counting Low Degree Number Fields with Almost Prescribed Successive Minima Speaker: Sameera Vemulapalli Affiliation: Princeton University Date: January 26, 2023 The successive minima of an order in a degree n number field are n real numbers encod
From playlist Mathematics
Square Root Problem: Solving the Quartic Equation!
blackpenredpen's video: https://youtu.be/cJAuOV9Dw5U Explanation of why x^2 + x - 5 is a factor: https://youtu.be/QPEh-1ScYAI The solution to this competition problem using a quadratic equation in "5" is awesome. How can we solve it without that method? Here we use some other strategies
From playlist Challenge Problems
KS5 - Cubic, Quartic & Reciprocal Graphs
"Graphs of more general functions, including reciprocal, cubic and quartic functions."
From playlist KS5 - Cubic, Reciprocal & Other Graphs
Isabel Vogt - An enriched count of the bitangents to a smooth plane quartic curve - AGONIZE
Recent work of Kass–Wickelgren gives an enriched count of the 27 lines on a smooth cubic surface over arbitrary fields, generalizing Segre’s signed count count of elliptic and hyperbolic lines. Their approach using 𝔸1-enumerative geometry suggests that other classical enumerative problems
From playlist Arithmetic Geometry is ONline In Zoom, Everyone (AGONIZE)
Watch more videos on http://www.brightstorm.com/math/precalculus SUBSCRIBE FOR All OUR VIDEOS! https://www.youtube.com/subscription_center?add_user=brightstorm2 VISIT BRIGHTSTORM.com FOR TONS OF VIDEO TUTORIALS AND OTHER FEATURES! http://www.brightstorm.com/ LET'S CONNECT! Facebook ► ht
From playlist Precalculus
Ila Varma, Counting quartic number fields and predicting asymptotics
VaNTAGe Seminar, June 14, 2022 License: CC-BY-NC-SA Links to some of the papers mentioned in this talk: Davenport-Heilbronn I: https://doi.org/10.1112/blms/1.3.345 Davenport-Heilbronn II: http://www.math.toronto.edu/~ila/DH2.pdf Wright: https://doi.org/10.1112/plms/s3-58.1.17 Baily: http
From playlist Arithmetic Statistics II
Livestream - Chapter 4 (4.1, 4.2): Graphs and transformations - AS/Year 12 Mathematics Revision
Join me in the live streams as I work through the AS/Year 12 content of the A-level curriculum. You can access the book I am using for free here: https://www.pearson.com/uk/learners/secondary-students-and-parents.html (you need to scroll down to "free e-book access") playlist: https:/
From playlist AS/Year 12 Summer Series
How to evaluate cotangent using a calculator
👉 Learn how to evaluate trigonometric functions using a calculator. To evaluate the trigonometric functions using a calculator, we just punch the necessary buttons on the calculator to obtain the result. While this may seem simple, most calculators only have sine, cosine and tangent avai
From playlist Trigonometric Functions and The Unit Circle
Graphing Polynomial Functions(HD)
Watch more videos on http://www.brightstorm.com/math/precalculus SUBSCRIBE FOR All OUR VIDEOS! https://www.youtube.com/subscription_center?add_user=brightstorm2 VISIT BRIGHTSTORM.com FOR TONS OF VIDEO TUTORIALS AND OTHER FEATURES! http://www.brightstorm.com/ LET'S CONNECT! Facebook ► ht
From playlist Precalculus
Introduction to Hyperbolic Functions
This video provides a basic overview of hyperbolic function. The lesson defines the hyperbolic functions, shows the graphs of the hyperbolic functions, and gives the properties of hyperbolic functions.
From playlist Using the Properties of Hyperbolic Functions