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