Quadratic Equations
There are several techniques for solving Quadratic Equations:
1) Factoring; 2) Square Root Property; 3) Completing the Square; 4) Quadratic Formula
I also list videos (see bottom) that show how to solve equations that are Quadratic in Form, or are radical equations or rational equations that become quadratic equations.
See below for videos on each method.
Go to the following link to see how to solve quadratic equations by factoring. This technique only works if the equation can be factored.
Solving Quadratic (and other non-linear Equations) by factoring
QE1: Solving Equations by Factoring 1: http://youtu.be/hadbOzKIdys
QE2: Solving Equations by Factoring 2: http://youtu.be/uvqFKHU-fjg
Watch this sequence of videos in order to understand and learn more methods you can use to solve quadratic equations, including using the square root property, completing the square, and the quadratic equation.
Below are videos showing how to solve quadratic equations using the Square Root Property of Equations. The videos have several examples.
QE3: Square Root Property of Equations 1
QE4: Square Root Property of Equations 2
QE5: Square Root Property of Equations 3
Below are videos showing how to solve quadratic equations by Completing the Square using Square Root Property of Equations. The videos have several examples.
QE6: Completing the Square 1
QE7: Completing the Square 2
QE8: Completing the Square 3
QE9: Completing the Square 4
QE10: Completing the Square 5
See also: *Completing the Square and Quadratic Formula 2 (below next video)
QE11: Completing the Square and Deriving the Quadratic Formula 1
In this video, we complete the square on a general quadratic equation in standard form to derive the quadratic formula, and learn a song sung to Pop goes the Weasel to help remember the Quadratic Formula.
QE12: *Completing the Square and Quadratic Formula 2
An example done both ways where coefficient of x-squared is 3
QE13: The Discriminant: This video defines the discriminant and shows how it is used to determine the kinds of solutions a quadratic equation has, without solving for the actual solutions.
Below are videos showing how to solve quadratic equations using the Quadratic Formula.
The videos have several examples.
QE14: Quadratic Formula 1
QE15: Quadratic Formula 2
QE16: Quadratic Formula 3
QE17: Quadratic Formula 4
QE18: Quadratic Formula 5
Below is the first video I made on the Quadratic Formula. It begins with the song, and then shows how to derive the Quadratic formula, and shows how to solve a problem using the quadratic formula. This has basically the same info as video QE11.
Quadratic Formula Song, How to derive the Quadratic Formula by completing the square, and one example using the quadratic formula
QE19: Writing Quadratic Equation from Solutions 1:
QE20: Writing Quadratic Equation from Solutions 2:
QE21: Writing Quadratic Equation from Solutions 3:
QE22: Writing Quadratic Equation from Solutions 4:
QE23: Writing Quadratic Equation from Solutions 5:
Videos showing how to solve equations that are Quadratic in Form, or how to solve rational or radical equations that become quadratic equations.
QE24: Solving a Radical Equation that becomes a Quadratic Equation 1
QE25: Solving a Rational Equation that becomes a Quadratic Equation 1
QE26: Solving a Rational Equation that becomes a Quadratic Equation 2
QE27Solving an Equation that is Quadratic in Form 1
QE28: Solving an Equation that is Quadratic in Form 2
QE29: Solving an Equation that is Quadratic in Form 3
QE30: Solving an Equation that is Quadratic in Form 4
Max and Min Problems--uses the idea of the vertex of a parabola to find a minimum or maximum value