Quadratic Equations

Quadratic Equations is Fx² + Ux + N

Definition – Quadratic equation is an equation in which the highest power of an unknown quantity is a square. It is a polynomial equation of the second degree.

What does it look like?

A ‘standard’ quadratic equation

                                                ax²  +  bx  +  c   =  0

Let’s break it down

  • The letters a, b and c are coefficients (you know those values). They can have any value, except that a cannot be 0. [Remember a coefficient is a number before a variable, x is the variable. It is unknown]
  • The letter “x” is the variable (you don’t know the value as yet)
 

Here is an example of one:

Give explanation as to why it is called a quadratic equation when it is only raised to the 2nd power. (Hint: word origination)

The solutions to the Quadratic Equation are where it is equal to zero. There are usually 2 solutions to the equation.

They are also called “roots”, or sometimes “zeros”

There are 3 ways to find the solutions:

1)      You can factor the Quadratic (find what to multiply to make the Quadratic Equation)

2)      You can complete the Square

3)      You can use the Quadratic Formula:

It is read “minus b plus or minus the square root of b-squared minus four ac, all over two a”

The entire formula can now be explained. The following website gives conceptual information in a fun way.

http://www.coolmath.com/algebra/09-solving-quadratics/05-solving-quadratic-equations-formula-02.htm

http://www.geogebra.org/en/wiki/index.php/Quadratic_Equations

Quadratic Rap – would no longer forget formula

http://www.youtube.com/watch?v=p1Jpdkf2HWY&feature=related

Project  and Exercise- use link

http://www.mrbenshoof.com/alg2Documents/Quadratic%20Equations%20Project.pdf

Using the Quadratic Formula solve the following problem

Just put the values of a, b and c into the quadratic Formula and, do the calculations, also graph the equation.

 5x² + 6x+ 1= 0

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