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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