Brian McLogan
Learn how to write a linear equation in polar form
Learn how to convert between rectangular and polar equations. A rectangular equation is an equation having the variables x and y which can be graphed in the rectangular cartesian plane. A polar equation is an equation defining an...
Brian McLogan
Finding the Zeros and Multiplicity of a Quadratic Function
👉 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...
Brian McLogan
How to take the derivative with chain rule inside product rule
👉 Learn how to find the derivative of a function using the chain rule. The derivative of a function, y = f(x), is the measure of the rate of change of the function, y, with respect to the variable x. The process of finding the derivative...
Brian McLogan
Given One Zero or Factor Find the Remaining Zeros
👉 Learn how to find all the zeros of a polynomial given one rational zero. 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...
Brian McLogan
How to determine the reduction scale factor for two parallelograms
👉 Learn about dilations. Dilation is the transformation of a shape by a scale factor to produce an image that is similar to the original shape but is different in size from the original shape. A dilation that creates a larger image is...
Curated Video
Naming Ordered Pairs in Exponential Functions
In this lesson, students will learn how to identify an ordered pair belonging to the same exponential function as two given ordered pairs. By understanding that exponential functions grow by equal factors on equal intervals, students can...
Brian McLogan
How to take the derivative of an equation implicitly
👉 Learn how to find the derivative of an implicit function. The derivative of a function, y = f(x), is the measure of the rate of change of the function, y, with respect to the variable x. The process of finding the derivative of a...
Curated Video
Finding the Center and Radius of a Circle using Completing the Square
In this video, the teacher explains how to find the center and radius of a circle when the equation is in general form. By using the process of completing the square, the teacher demonstrates how to transform the equation into standard...
Brian McLogan
Solve a trigonometric equation using the double angle formulas
👉 Learn how to use the double angle identities to solve trigonometric equations. When we have equations with a double angle we will apply the identities to create an equation that can help solve by inverse operations or factoring. We...
Curated Video
Understanding Multiplication as Area: Using a Multiplication Table
In this lesson, students will learn how to represent products as areas using a multiplication table. They will understand that the product of two factors can be found by matching the row and column of the multiplication table.
Science360
Self-control
In (Thanksgiving-inspired) episode 34, Charlie and Jordan explore how your ability to exercise self-control may depend on how quickly your brain factors healthfullness into food choices.
Science360
Insect battles provide clues to evolution
The seemingly peaceful atmosphere in an organic garden on the University of Florida campus belies the battles happening among many of its tiniest inhabitants -- the insects. For entomologist Christine Miller, there are endless...
Brian McLogan
Rationalizing the radical to evaluate the limit
👉 Learn how to evaluate the limit of a function by rationalizing the radical. The limit of a function as the input variable of the function tends to a number/value is the number/value which the function approaches at that time. The limit...
Brian McLogan
Learn to implicitly differentiate an equation and define through a point
👉 Learn how to find the derivative of an implicit function. The derivative of a function, y = f(x), is the measure of the rate of change of the function, y, with respect to the variable x. The process of finding the derivative of a...
Brian McLogan
Determining the roots of a quadratic equation by factoring when a is not one
we find two factors of the product of the constant term (the term with no variable) and the coefficient of the squared variable whose sum gives the linear term. These factors are now placed in separate brackets with x to form the factors...
Curated Video
Calculating Exponential Growth and Decay
In this video, the teacher explains how to create and solve simple exponential functions by examining exponential growth and decay problems. Using the example of bacteria growing on a toothbrush, the teacher demonstrates how to calculate...
Brian McLogan
How to find the domain of a rational function - domain and range
👉 Learn how to find the domain of rational functions. Recall that the domain of a function is the set of possible input values (x-values) of the function. For a rational function, the denominator cannot be zero. Thus, to find the domain...
Brian McLogan
Use baby numbers to evaluate the right hand limit of a rational function
👉 Learn how to evaluate the limit of a function involving rational expressions. The limit of a function as the input variable of the function tends to a number/value is the number/value which the function approaches at that time. The...
Curated Video
Completing the Square: Algebraic Method for a > 1
In this video, the teacher explains how to complete the square when the coefficient of the quadratic term is greater than one. They demonstrate the process using algebraic steps and provide examples for better understanding.
Brian McLogan
Learn how to determine concavity and point of inflection AP style
👉 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...
ShortCutsTv
Natural Experiments
How do natural experiments differ from Field or Laboratory experiments? Are there different types and what does this research method give to psychologists that other methods don't? This film examines these questions in the context of...
Professor Dave Explains
The Complement System: Classical, Lectin, and Alternative Pathways
We are learning about the features of innate immunity, and one that is often overlooked is the complement system. This is a very complicated ensemble of proteins circulating in the bloodstream that activate each other in a specific...
Brian McLogan
Find All the Remaining Rational Zeros Given One Zero
👉 Learn how to find all the zeros of a polynomial given one rational zero. 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...
Brian McLogan
Learn how to find the critical values of a polynomial
👉 Learn how to find the critical values of a function. The critical values of a function are the points where the graph turns. They are also called the turning points of a function. To obtain the critical points of a function, first, we...