Solving Quadratic Equations

To solve a Quadratic Equation in the form:

I. Factoring Technique:

1. Set the equation equal to zero.

2. Factor the non-zero side.

3. Set each factor that has a variable equal to zero.

4. Solve for the variable.

II. Square Root Property Technique:

If the quadratic equation is in the form:

1. Take the square root of both sides of the equation and solve for the variable.

III. Completing the square:

1. Isolate the x-terms, and make sure the coefficient of is 1

2. Complete the square: Take of the coefficient of x , then square that

result, add the second result to both sides of the equation

3. Factor into the form:

4. Use the square root property to solve the equation.

(Take the square root of both sides of the equation and solve for the

variable.)

IV. Quadratic Formula Technique:

1. Set the equation equal to zero.

2. Determine the values of a, b, and c.

3. Substitute a, b, and c into the quadratic formula:

4. Solve for x.

Note: is called the discriminant.

If: (or positive) 2 real solutions

1 real solution

(or negative) 2 imaginary solutions

V. Quadratic Equations can also be solved using the calculator:

1. Graph the equation. Find where the equation crosses the x-axis.

***If the graph does not cross the x-axis, this means there are 2 imaginary

solutions.

These kinds of solutions must be found using a different technique such as the

Quadratic Formula (by hand) or by using POLY on the calculator.

***If the graph touches the x-axis in just one point, the solution is that x-intercept

with multiplicity of 2.