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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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