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Find the Vertex by Using the Quadratic Formula

The Quadratic Formula is primarily used to identify the roots (\(x\)-intercepts) of a quadratic function. What many people don't know is that you can also easily find the vertex of the function by simply looking at the Quadratic Formula! Graphing Quadratic Functions When graphing quadratic...

Completing the Square

Introduction A brief discussion about what completing the square is and what we use it for. Focuses on using the technique for other reasons than solving equations. Background Math Development of the patterns we use for completing the square. This part is important since it introduces the notation...

Cardinality and Countably Infinite Sets

Cardinality is a term used to describe the size of sets. Set A has the same cardinality as set B if a bijection exists between the two sets. We write this as |A| = |B|. One important type of cardinality is called “countably infinite.” A set A is considered to be countably infinite if a bijection...

The Quadratic Equation

The quadratic equation is always the answer. Time and time again, while tutoring students, I encounter a resistance to using an unfailing tool called the quadratic equation. This simple algebraic mathematical statement allows a student to find the roots of any clumsy second order polynomial with...

Navier-Stokes is hard?

Navier-Stokes is hard? Author: James Lowman I was recently asked the question; "How can the Navier-Stokes equations both describe our observable world and not be known to always have solutions in 3D?" For those that don't know, the Navier-Stokes (NS) equations represent a mathematical model that...

The Natural Logarithm Rules

The natural logarithm, whose symbol is ln, is a useful tool in algebra and calculus to simplify complicated problems. In order to use the natural log, you will need to understand what ln is, what the rules for using ln are, and the useful properties of ln that you need to remember. What is the...

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