This document discusses quadratic equations. It defines a quadratic equation as having the standard form ax^2 + bx + c, where a, b, and c are constants and x is the variable. It describes three methods for solving quadratic equations: factoring, completing the square, and using the quadratic formula. Factoring works when the equation can be rewritten as a product of two binomials. Completing the square is used when factoring is not possible. It involves rearranging terms to create a perfect square trinomial. The quadratic formula can be used to solve any quadratic equation by substituting the a, b, and c values.

1. Arnulfo Peña
Herma Araujo

2. What is a quadratic equation?
 The name quadratic zome from “squad” meaning
square, the variable get squared (over 2)
 The standard form of a quadratic equation is:
ax´2 + bx + c
 The assumptions are:
 a, b and c are known values. a can't be 0.
 "x" is the variable or unknown (you don't know it
yet).

3. Hidden quadratic equations

4. How to solve quadratic equations
 There are 3 ways to find the solutions:
 1. You can Factor the Quadratic (find what to multiply
to make the Quadratic Equation)
 2. You can Complete the Square
 3. You can use the special Quadratic Formula:

5. Solving quadratic equations by
factorizing
 Having an easy quadratic formula, factorizing become
a easy and fast method:
 Having: x2 + 10x + 25
 Can factorized as (x+5) (x+5)
 Now by making each equation equal “0”
 X+5 = 0, x = -5

6. Solving by complete the square
 Completing the square is used when the equations
doesn’t have a “c” value
 Having: x2 + 4x + 1 = 0
 The equation cannot be factorizing therefore is
necesarry complet the square

7.  Step 1: Passing to the other side the “c” value
x2 + 4x = -1
 Step 2: Using the formula (B/2)2 obtain the real “c”
value
(4/2)2 = 4
 Step 3 : Sum the “c” value to both sides of the equation.
x2 + 4x + 4 = -1+ 4
 Step 4: Factorize the trinomial equation
(x+2)2 = 3
 Solve the quation by square root

8. Solving by the quadratic formula
 In order to solve difficult equations, quadratic formula
is used:
 It is used by substituting each value: a, b and c
according to the equation given.

9. *Completing the Square (Completing the Square)
http://www.mathsisfun.com/algebra/completing-square.html
*Quadratic equations. (2000, January 1). . Retrieved May 29, 2014,
from http://mathworld.wolfram.com/QuadraticEquation.html