Group Practice - What Do You Remember?

Quadratic Equations using Quad. Formula

Practice Using Quadratic Formula (Use a calculator)

Practice Factoring Quadratic Equations

quad. equations using Completing the Square

Completing the Square is another way to solve quadratic equations.

Given x² + 4x + 1 = 0

Check for the following:

1. The x² term must have a coefficient of 1. If it doesn't, divide the entire equation (BOTH SIDES) by the coefficient to make it 1.

2. Move the constant to the other side of the equation, away from the x² term.

x² + 4x = -1

3. Take 1/2 of the linear term coefficient ( the x term) , square it, and add it to BOTH sides of the equation. x² + 4x + (4/2)² = -1 + (4/2)²

x² + 4x + 4 = -1 + 4

x² + 4x + 4 = 3

4. Factor the quadratic (x + 2)(x+2) = 3

(x+2)² =3

5. Square root both sides of the equation. Remember, that a square root will give you BOTH a positive (+) and negative (-) answer. x + 2 = ±√3

6. Solve by isolating the variable. x = -2 ±√3

x = -2 + √3 or x = -2 - √3

7. Remember, the solutions to a quadratic equation are the x-intercepts of the graph of that equation's function.

Let's do another:

Completing the Square is another way to solve quadratic equations.

Given x² + 6x - 16 = 0

Check for the following:

1. The x² term must have a coefficient of 1. If it doesn't, divide the entire equation (BOTH SIDES) by the coefficient to make it 1.

2. Move the constant to the other side of the equation, away from the x² term.

x² + 6x = 16

3.Take 1/2 of the linear term coefficient ( the x term) , square it, and add it to BOTH sides of the equation. x² + 6x + (6/2)² = 16 + (6/2)²

x² + 6x + 9 = 16 + 9

x² + 6x + 9 = 25

4. Factor the quadratic (x + 3)(x+3) = 25

(x+3)² =25

5. Square root both sides of the equation. Remember, that a square root will give you BOTH a positive (+) and negative (-) answer. x + 3 = ±√25

6. Solve by isolating the variable. x = -3 ±√25

x = -3 +5 or x = -3 - 5

x = 2 or x = -8

Practice Using Completing the Square