Algebra
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Quadratics
Solving quadratics through factoring, completing the square, graphing, and the quadratic equation.
Tutorials
Factoring quadratics
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Just saying the word "quadratic" will make you feel smart and powerful. Try it. Imagine how smart and powerful you would actually be if you know what a quadratic is. Even better, imagine being able to completely dominate these "quadratics" with new found powers of factorization. Well, dream no longer.
This tutorial will be super fun. Just bring to it your equation solving skills, your ability to multiply binomials and a non-linear way of thinking!
- Factoring quadratic expressions
- Examples: Factoring simple quadratics
- Example 1: Factoring quadratic expressions
- Factoring polynomials 1
- Example 1: Solving a quadratic equation by factoring
- Example 2: Solving a quadratic equation by factoring
- Example 3: Solving a quadratic equation by factoring
- Example 4: Solving a quadratic equation by factoring
- Example: Graphing a quadratic
- Solving quadratics by factoring
- Example 1: Factoring trinomials with a common factor
- Factoring polynomials 2
- Solving quadratics by factoring 2
- Factoring Special Products
- Example 1: Factoring difference of squares
- Example 2: Factoring difference of squares
- Factoring difference of squares 1
- Factoring difference of squares 2
- Factoring difference of squares 3
- Example: Factoring perfect square trinomials
- Example: Factoring a fourth degree expression
- Example: Factoring special products
- Factor by Grouping and Factoring Completely
- Graphs of Quadratic Functions
- Example: Basic grouping
- Example 1: Factoring by grouping
- Example 2: Factoring by grouping
- Example 3: Factoring by grouping
- Example 4: Factoring by grouping
- Example 5: Factoring by grouping
- Example 6: Factoring by grouping
- Factoring polynomials by grouping
- Factoring polynomials with two variables
Completing the square
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You're already familiar with factoring quadratics, but have begun to realize that it only is useful in certain cases. Well, this tutorial will introduce you to something far more powerful and general. Even better, it is the bridge to understanding and proving the famous quadratic formula.
Welcome to the world of completing the square!
- Solving Quadratic Equations by Square Roots
- Example: Solving simple quadratic
- Solving quadratics by taking the square root
- Solving Quadratic Equations by Completing the Square
- Completing the square (old school)
- Example: Completing perfect square trinomials
- Example 1: Completing the square
- Example 2: Completing the square
- Example 3: Completing the square
- Example 4: Completing the square
- Example 5: Completing the square
- Completing the square 1
- Completing the square 2
The quadratic formula (quadratic equation)
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Probably one of the most famous tools in mathematics, the quadratic formula (a.k.a. quadratic equation) helps you think about the roots of ANY quadratic (even ones that have no real roots)! As you'll see, it is just the by-product of completing the square, but understanding and applying the formula will take your algebra skills to new heights.
In theory, one could apply the quadratic formula in a brainless way without understanding factoring or completing the square, but that's lame and uninteresting. We recommend coming to this tutorial with a solid background in both of those techniques. Have fun!
- How to Use the Quadratic Formula
- Example: Quadratics in standard form
- Proof of Quadratic Formula
- Example 1: Using the quadratic formula
- Example 2: Using the quadratic formula
- Example 3: Using the quadratic formula
- Example 4: Applying the quadratic formula
- Example 5: Using the quadratic formula
- Quadratic formula
- Example: Complex roots for a quadratic
- Discriminant of Quadratic Equations
- Discriminant for Types of Solutions for a Quadratic
- Solutions to quadratic equations
Graphing quadratics
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Tired of lines? Not sure if a parabola is a disease of the gut or a new mode of transportation? Ever wondered what would happen to the graph of a function if you stuck an x² someplace? Well, look no further.
In this tutorial, we will study the graphs of quadratic functions (parabolas), including their foci and whatever the plural of directrix is.
- Ex 3: Graphing a quadratic function
- Example: Graphing a quadratic
- Example: Roots and vertex of a parabola
- Example: Parabola vertex and axis of symmetry
- Graphs of Quadratic Functions
- Examples: Graphing and interpreting quadratics
- Applying Quadratic Functions 1
- Applying Quadratic Functions 2
- Applying Quadratic Functions 3
- Graphing parabolas in standard form
- Parabola Focus and Directrix 1
- Focus and Directrix of a Parabola 2
- Vertex of a parabola
- Graphing parabolas in vertex form
- Graphing parabolas in all forms
- Parabola intuition 3
Quadratic inequalities
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You are familiar with factoring quadratic expressions and solving quadratic equations. Well, as you might guess, not everything in life has to be equal.
In this short tutorial we will look at quadratic inequalities.
Quadratic odds and ends
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This tutorial has a bunch of extra, but random, videos on quadratics. A completely optional tutorial that you may or may not want to look at. If you do, watch it last. There are some Sal oldies here and some random examples.
- Solving a quadratic by factoring
- CA Algebra I: Factoring Quadratics
- Algebra II: Quadratics and Shifts
- Examples: Graphing and interpreting quadratics
- CA Algebra I: Completing the Square
- Introduction to the quadratic equation
- Quadratic Equation part 2
- Quadratic Formula (proof)
- CA Algebra I: Quadratic Equation
- CA Algebra I: Quadratic Roots