Solving Quadratic Equations

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Quadratic Equations

This lens is designed for students, parents and teachers to supplement instruction on quadratic equations. There are video examples for all the topics to go along with the text explanations. To find you topic either scroll down or use the table of contents below.

If you are a teacher looking for resoureces check out my math teaching website. There are some very good worksheets.

Though I think this lens is valuable and can really help you understand quadratic equations sometimes it isn't enough. One of the most effective ways to learn math is one on one tutoring. Tutor.com offers 25 minutes for FREE and is something you should definitely check out.


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Solving Basic Quadratic Equations 

Quadratic Equations - Any single variable equation where the highest power is two. The simplest type of quadratic equation occurs when there is one variable with power two and no other variables.

Procedure - Basic Quadratic Equations

1) Solve the equation so that the x-squared(or whatever variable in the problem) term is by itself on one side of the equation with coefficient one.

2) Take the square root of both sides. On the side with the number be sure to add +/-, because the positive and negative value will solve the equation.

3) Simplify the right side of the equation by simplifying the square root.

Special Case - When you solve for the variable squared if the other side is negative the answer is "no real solution". It is not possible to find a real square root of a negative number.

The following videos show examples of how to apply this procedure.

Solving Basic Quadratic Equations Example 1 

A19.9 Solving Simple Quadratic Equations

From http://www.squidoo.com/quadraticequations the following is a video showing how to solve simple quadratic equations. For more math help check out www.teachingandlearningmath.blogspot.com

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Solving Basic Quadratic Equations Example Set 2 

A19.10 Basic Quadratic Equations

From http://www.squidoo.com/quadraticequations the following are a couple of examples of solving basic quadratic equations by taking the square root of both sides. For more math help check out www.teachingandlearningmath.blogspot.com

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Solving Basic Quadratic Equations Example Set 3 

A19.11 Solving Basic Quadratic Equations

From http://www.squidoo.com/quadraticequations the following is a couple of examples of how to solve simple quadratic equations. For more math help check out www.teachingandlearningmath.blogspot.com

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Graphing Quadratic Equations (Parabolas) 

Just like linear equations it important to look at the graph of quadratic equations. The graph of a quadratic equation is referred to as a parabola and has the general shape of a cross between a "u" and a "v".

There are two specific ways to graph quadratic equations. In this section we will be looking at using a table of values to determine the graph. In order to do this we have to determine what the vertex is. The vertex is the point at the bottom(or top) of the parabola.

We start by finding the "x" coordinate of the vertex. The formula for finding this is x = -b/2a. The a and b come from y = ax2+bx+c. Once the x coordinate of the vertex is determined it is placed on the table of values in such a way that two more values can be placed above it and two below.

The next step is to fill those empty x-values by counting up and down from the x-coordinate of the vertex. Once you have done this you fill in the table of values by plugging the x-values into the original equations and finding the y-values. After you have done this you graph the points and draw in the graph.

Graphing Quadratic Equations (Parabolas) Example 1 

The following example show a basic way to graph quadratic equations.

A19.16 Graphing Quadratic Equations

From http://www.squidoo.com/quadraticequations the following shows how to graph a qaudratic equation (Parabola). For more math help check out www.teachingandlearning.blogspot.com

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Graphing Quadratic Equations (Parabola's) Example 2 

The following is an example of how to graph quadratic equations using a basic method.

A19.17 Graphing Quadratic Equations

From http://www.squidoo.com/quadraticequations this is an example how to graph a quadratic equation(parabola). For more math help checkout www.teachingandlearningmath.blogspot.com

Runtime: 181
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A graphing calculator is an essential learning tool for learning Algebra, Precalculus and Calculus.

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Solving Quadratic Equations Using the Quadratic Formula 

The most common method of solving quadratic equations is using the quadratic formula. The quadratic formula is used with the standard form of a quadratic equation which is ax2+bx+c=0. The quadratic formula is:



It is key to first figure out a,b and c. To do this you solve the quadratic equation for zero. The number in front of the x2 is a, the number in front of x is the b and the number that is by itself is c.

The following video examples show how to find the solutions to a quadratic equation using the quadratic formula.

Don't Forget!!!!

Use ax2+bx+c=0 to find out a, b, and c. a is in front of the x squared term b is in front of the x and c is the part without a variable.

Solving Quadratics Equations Using the Quadratic Formula Example 1 

A19.12 Using the Quadratic Formula

From http://www.squidoo.com/quadraticequations the following is an example of how to solve a quadratic equation using the quadratic formula. For more math help check out www.teachingandlearningmath.blogspot.com

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Solving Quadratic Equations Using the Quadratic Formula Example 2 

A19.13 Quadratic Formula

From http://www.squidoo.com/quadraticequations the following shows how to solve quadratic equations using the quadratic formula. For more math help check out www.teachingandlearningmath.blogspot.com

Runtime: 163
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Solving Quadratic Equations Using the Quadratic Formula Example 3 

A19.14 Quadratic Formula

From http://www.squidoo.com/quadraticequations the following is an example of how to use the quadratic formula to solve quadratic equations. For more math help check out www.teachingandlearningmath.blogspot.com

Runtime: 118
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Solving Quadratic Equations Using the Quadratic Formula Example 4 

A19.15 Using the Quadratic Formula

From http://www.squidoo.com/quadraticequations the following video is an example of how to simplify quadratic equations. For more math help check out www.teachingandlearningmath.blogspot.com

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The Derivation of the Quadratic Formula 

The following video shows how to derive the quadratic formula by completing the square.

Derivation of the Quadratic Formula

From http://www.squidoo.com/quadraticequations the following shows how to derive the quadratic formula by completing the square. For more math help check out www.teachingandlearningmath.blogspot.com

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Solving Quadratic Equations by Factoring 

A third way to solve quadratic equations is to solve by factoring. This is based on the Multiplication Propert of Zero.

Multiplication Property of Zero

If a*b = 0 then either a = 0 or b = 0.

Thus we set the quadratic equation equal to zero and factor. Once we have factored the quadratic equation then we set each factor equal to zero. We do this because when one of the two factors is equal to zero then the quadratic equation is equal to zero.

Watch the following videos to see some examples of how to solve quadratic equations by factoring.

Solving Quadratic Equations by Factoring Example Set 1 

A110.1 Solving Quadratic Equations by Factoring

From http://www.squidoo.com/quadraticequations the following is an example of how to solve quadratic equations by factoring. For more math help check out www.teachingandlearningmath.blogspot.com

Runtime: 119
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Solving Quadratic Equations by Factoring Example Set 2 

A110.2 Solving Quadratic Equations by Factoring

From http://www.squidoo.com/quadraticequations the following is an example of how to solving quadratic equations by factoring. For more math help check out www.teachingandlearningmath.blogspot.com

Runtime: 189
1751 views
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Quadratic Equation Worksheets 

Using the Quadratic Formula
Eight problems using the quadratic formula to solve quadratic equations.
Basic Quadratic Equations
Nine problems on solving basic quadratic equations. No "x" term.

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My name is Trent Tormoehlen and I am a math teacher at Sycamore School in Indianapolis Indiana.  I will also be helping coach the schools Math Co...

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