# Quadratic Formula and Quadratic Equations

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A series of free, online Intermediate Algebra Lessons or Algebra II lessons.

Videos, worksheets, and activities to help Algebra students.

### Deriving the Quadratic Formula

The quadratic formula is one of the most important formulas that you will learn in Algebra and chances are that you have probably memorized it. But where does it come from? When deriving the quadratic formula, we first start with a generic quadratic formula using coefficients a, b and c and then derive the formula by completing the square.

This video shows the proof of the quadratic formula by solving ax^{2} + bx + c by completing the square.

### Overview of the Different Methods of Solving a Quadratic Equation

Solving quadratic equations can be difficult, but luckily there are several different methods that we can use depending on what type of quadratic that we are trying to solve. The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula.

More details about the methods used to solve a quadratic equation.

How to know which method to use when solving a quadratic equation.

### The Discriminant of a Quadratic Equation

The discriminant is part of the quadratic formula which lies underneath the square root. The quadratic equation discriminant is important because it tells us the number and type of solutions. This information is helpful because it serves as a double check when solving quadratic equations by any of the four methods (factoring, completing the square, using square roots, and using the quadratic formula).

A discussion on what the discriminant is, how it's used, and it's connection to graphs of quadratic functions.

### Solving Quadratic Equations in Disguise

There are four methods to solving quadratic equations: factoring, completing the square, using square roots, and using the quadratic formula. Sometimes there are more complex quadratic equations including equations that have fractional exponents and negative exponents. To solve these types of problems, we either make a substitution for a term or factor out negative exponents.

Using quadratic methods to solve quadratic equations and exponential equations that can be modified to look like quadratics.

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