Warm-Up: September 30 / October 1, 2015 Factor each expression 2x2 + 7x – 4 4x2 – 13x + 3 9x2 + 9x + 2

Homework Questions?

Quadratic Equations Section P.8

Essential Question How can we solve quadratic equations?

Quadratic Equations A quadratic is a second-degree polynomial The general form is

Zero Product Property If AB = 0, then A = 0 or B = 0 Use to solve a quadratic Write the quadratic in general form Factor the quadratic Set each factor equal to zero Solve each equation

You-Try #1: Solve by Factoring

Solving Quadratics Using Square Roots Use when you have x2 + c = 0 (b=0) Also used when you have an expression squared and a number (u2=d) Get the squared term by itself Take the square root of both sides Remember ±

You-Try #2: Solve with Square Root

Completing the Square Given 𝑥 2 +𝑏𝑥, we can create a perfect square trinomial by dividing b by 2, squaring it, and adding it When solving, you must have one side be “ 𝑥 2 +𝑏𝑥” Remember that whatever you add to one side, you must add to the other side

Example 3: Completing the Square (#27-37) Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial

You-Try #3: Completing the Square (#27-37) Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial

Example 4a: Solving by Completing the Square

You-Try #4: Solving by Completing the Square

Example 4b: Solving by Completing the Square

The Quadratic Formula

You-Try #5: Solving using Quadratic Formula

The Discriminant: b2 – 4ac The value of the discriminant tells you the number and type of solutions you will have Discriminant Solutions to ax2 + bx + c = 0 b2 – 4ac < 0 b2 – 4ac = 0 b2 – 4ac > 0 Is a perfect square Not a perfect square

The Discriminant: b2 – 4ac The value of the discriminant tells you the number and type of solutions you will have Discriminant Solutions to ax2 + bx + c = 0 b2 – 4ac < 0 No real solutions b2 – 4ac = 0 One real solution b2 – 4ac > 0 Is a perfect square Two rational solutions Not a perfect square Two irrational solutions

Example 6: Using the Discriminant (#63-69) Compute the discriminant. What does the discriminant indicate about the number and type of solutions?

You-Try #6: Using the Discriminant (#63-69) Compute the discriminant. What does the discriminant indicate about the number and type of solutions?

What method should I use? If 𝑎 𝑥 2 +𝑏𝑥+𝑐 can easily be factored, then factor and use zero product property. If 𝑏=0, use square root method If you have something in parentheses squared, use square root method. If 𝑎 𝑥 2 +𝑏𝑥+𝑐 cannot be factored, use quadratic formula See page 94 if you need more help choosing what method to use.

Assignment Read Section P.8 Page 97 #1-93 Every Other Odd, 99, 119