What is the Quadratic Formula?
The quadratic formula is :
What does this formula tell us?
The quadratic formula will calculate the solutions of any quadratic equation.
What is a quadratic equation?
A quadratic equation is an equation that can be written as ax ² + bx + c where a ≠ 0 In other words, a quadratic equation must have a squared term as its highest power Examples of quadratic equations
 y = 5x² + 2x + 5
 y = 11x² + 22
 y = x²− 4x +5
 y = −x² + 5
 y = 11x + 22
 y = x^{3} − 4x² +5x +5
 y = 2x^{3} − 4x²
 y = −x^{4} + 5
Ok, but what is a 'solution'?
Well a solution can be thought in two ways:
Algebra:  For any quadratic equation of the form f(x) = ax^{2}+bx+c, the solution is when f(x) = 0. 
Geometry  The solution is where the graph of a quadratic equation (a parabola) is intersects the xaxis.

Example of the quadratic formula to solve an equation
Quadratic Equation: y = x² + 2x + 1, a = 1, b = 2, c = 1
Using the quadratic formula to solve this equation just substitute a,b, and c into the general formula:
Below is a picture representing the graph of y = x² + 2x + 1 and its solution
Quadratic Formula Song
A catchy way to remember the quadratic formula is this song (pop goes the weasel)
Practice Problems
 a =1
 b = − 2
 c = 1
In this quadratic equation,y = x² − x − 2 and its solution
 a =1
 b = − 1
 c = − 2
In this quadratic equation, y = x² − 1 and its solution
 a = 1
 b = 0
 c = −1
In this quadratic equation, y = x² + 2x − 3 and its solution
 a =1
 b = 2
 c = −3
Below is a picture of the graph of the quadratic equation and its two solutions
In this quadratic equation, y = x² + 4x − 5 and its solution
 a =1
 b = 4
 c = −5
In this quadratic equation,y = x² − 4x + 5 and its solution
 a =1
 b = −4
 c = 5
Below is a picture of this quadratic's graph