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The quadratic formula
 Objective: To solve quadratic equations by using the quadratic formula

The quadratic formula can be used to find the solutions of any quadratic equation. Every quadratic equation can be written in the standard form ax2 + bx + c = 0. This form can be solved for x by completing the square. Begin by subtracting x from both sides.
The Quadratic Formula: where a is a positive number the solutions of a quadratic equation in standard form ax2 + bx + c, the formula is as follows:


x =

Note that this equation will give two solutions; one negative, the other positive. This is because of the + sign.

Example:
Solve 2y +1 = 2y2 by the quadratic formula.
First, put the equation in standard form.
2y +1 = 2y2
2y2 - 2y - 1 = 0
Now, use the quadratic formula--   a will equal 2, b will equal -2, and c will equal -1
If you plug all the numbers in and simplify, the result will be:

There are 4 methods for solving quadratic equations:
(1) Square root property
(2) Factoring
(3) Completing the square
(4) Quadratic formula
Methods (3) and (4) can be used for any quadratic equation, but methods (1) and (2) are used when an equation has no middle term.