1. A.5 B. Solving Quadratic Equations A.5 B. Solving Quadratic Equations Objectives: 1.Factoring 2.Square Root Method 3.Completing the Square 4.Quadratic Formula 5. Use the discriminant to determine the number of solutions. Objectives: 1.Factoring 2.Square Root Method 3.Completing the Square 4.Quadratic Formula 5. Use the discriminant to determine the number of solutions.

2. Vocabulary Solving Quadratic Equations A quadratic equation has the form where a, b, and c are real numbers and a ≠ 0 Topic for Discussion: You know that if ab=0, then a=0 or b=0. Suppose a polynomial is written in factored form and set to zero. For instance, What must x be in order for this to be a true statement? What can be said about any polynomial written as a product of linear factors and set to zero? Topic for Discussion: You know that if ab=0, then a=0 or b=0. Suppose a polynomial is written in factored form and set to zero. For instance, What must x be in order for this to be a true statement? What can be said about any polynomial written as a product of linear factors and set to zero?

3. 4 methods to solve a quadratic MethodPros ConsExample Factoring Square Root Complete the Square Quadratic Formula

4. Factoring 1. Solve by Factoring. To solve by factoring: 1)Move everything to one side: Get in standard form 2)Factor Zero-Product Property 3)Apply the Zero-Product Property: If A and B are algebraic expressions and if AB=0, then A=0 or B=0. To solve by factoring: 1)Move everything to one side: Get in standard form 2)Factor Zero-Product Property 3)Apply the Zero-Product Property: If A and B are algebraic expressions and if AB=0, then A=0 or B=0. Examples If an expression factors easily, this is the preferred method.

5. 2. Solve by the Square Root Method this is the preferred method. Examples Isolate the or part to one side and take square root. Don’t forget the !!

6. 3. Solve by Completing the Square 1: Move c to the other side 2: Add to both sides 3: 4: solve with square root method Pre-Step 1: If the coefficient in front of is not 1, factor it out. GOAL: Rewrite as a perfect square and apply the square root method.

7. Completing the Square More practice….Completing the Square

8. 4. Quadratic Formula Given the quadratic equation where a ≠ 0 the solutions are given by the quadratic formula:

9. Apply the Quadratic Formula 1. Solve using the quadratic formula

10. The discriminant of the quadratic is the value of: The number of solutions can be determined by the value of the discriminant If, there are NO real solutions If, there is a repeated real solution If, there are 2 real solutions The discriminant of the quadratic is the value of: The number of solutions can be determined by the value of the discriminant If, there are NO real solutions If, there is a repeated real solution If, there are 2 real solutions 5. The discriminant Recall: quadratic formula

11. 4. a) The discriminant Example: 1. What is the discriminant for this equation? 2. What does it tell us about the number of solutions?

12. Activity: Prove the quadratic formula.

13. Methods for solving a quadratic Form of the quadratic equation Most efficient methodExample can be factored easily Factor and use zero- product principle Factor out the x and use the zero-product principle Solve for and apply square root method where u is a 1 st degree polynomial square root method cannot be factored complete the square or quadratic formula

14. x xb/2 1.What is the area of rectangle 1 = rectangle 2 = rectangle 3 = 2. What would the dimension of the corner square need to be to “complete the square”? Making a Perfect Square 12 3 4 3. What is the area of the Large Square?