Bell Ringer (in your Math Journal) 1. What are the 3 forms of the graphs of quadratics? 2. What are the 4 names for the answers of a quadratic equation? 3. What must a quadratic equation be equal to before you can factor it?

The Discriminant, the Quadratic Formula, and Completing the Square Thursday October 1, 2015

Standard Form of a Quadratic Equation

The Discriminant

The Discriminant The Discriminant is: Way to solve: Number and kind of solutions Positive and Square Factor 2 Rational Zero 1 Rational Positive not square Quadratic formula or Complete the square 2 Irrational Negative 2 Imaginary Solutions

Picture: Positive Discriminant 2 Real Solutions

Picture: Zero Discriminant 1 Real Solution “Double root”

Picture: Negative Discriminant 0 Real Solution. 2 Complex Solutions.

Using the discriminant

Using the discriminant

Now we can find the square root of a negative!

Using the discriminant

Using the discriminant

  Steps for Completing the Square 1) Write the quadratic in Standard Form 2) Divide all terms by “a” 3) Move the constant to the right side of the equation 4) Add (b/2)2 to both sides of the equation to make the left a perfect square trinomial 5) Write the left in factored form 6) Take the square root of both sides 7) Subtract the constant from both sides to get x =

Ex: 2x2 – 4x = 6 Step 1) 2x2 – 4x – 6 = 0 Step 2) x2 – 2x – 3 = 0 Step 3) x2 – 2x = 3 Step 4) x2 – 2x + 1 = 3 + 1 Step 5) (x – 1)2 = 4 Step 6) x – 1 = +/- 2 Step 7) x = 3, -1

Classwork: Solving Quadratics in Various Ways Some with Complex Solutions Discriminant (1-4), Quadratic Formula (1-4), Completing the Square (1-4) Homework: Discriminant and Solving Quadratics Using Any Method