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Solving Quadratic Equations by Factoring
ZERO FACTOR PRINCIPLE :
if and only if 
Solving quadratic equations by factoring:
1. Write the equation in form.
2. Factor the nonzero side of the equation.
3. Use the zero factor principle to set each factor equal to zero .
4. Solve each resulting linear equation.
The Quadratic Formula : The solutions of the equation are
The Discriminant is
(the expression underneath the radical sign ).
Let D represent the Discriminant. In other words, .
number and type of solutions 
number of x  intercept points 

two complex (conjugate) solutions 
none  
exactly one real solution 
exactly one ( it is the vertex ) 

exactly two distinct real solutions 
exactly two 
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