Lesson 9.3 Using the Quadratic Formula to solve equations

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Solving Quadratic Equations by the Quadratic Formula

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Presentation transcript:

Lesson 9.3 Using the Quadratic Formula to solve equations Please tear our your 9.3 packet…pages 381-394

THE QUADRATIC FORMULA The quadratic formula is used when the quadratic cannot easily be factored. The quadratic formula can be used to solve ANY quadratic!!

The Discriminant The discriminant allows us to find out how many, and what type of solutions we have to any quadratic function.

The Discriminant The Discriminant can be negative, positive or zero If the Discriminant is positive, there are 2 real answers. If the Discriminant is zero, there is 1 real answer. If the Discriminant is negative, there are 2 complex answers. complex answer have i.

Example 1: Find the number and type of solutions Step 1: Make sure the quadratic is in standard form. Step 2: Plug in a, b, and c, into the discriminant. Since the 76 is positive, we can say that this quadratic has 2 real solutions.

Example 2: Find the number and type of solutions Since the 7 is negative, we can say that this quadratic has NO real solutions.

Example 3: Find the number and type of solutions Since the solution is negative, we can say that this quadratic has NO real solutions.

Steps to solve using the quadratic formula: Step 1: Make sure the quadratic is put into standard form. Step 2: Identify a, b, and c. Step 3: Plug a, b, and c into the quadratic formula. **Don’t forget to use your parentheses!!** Step 4: Simplify. **Be careful! Take your time and watch out for your positive and negative signs!**

Example 4: Solve using the quadratic formula Step 1: Make sure it is in standard form. Step 2: Identify a, b, and c. a = 1 b = -5 c= 6

Example 4 (cont.) Step 3: Plug it into the formula….(don’t forget parentheses!)

Example 4 (cont.) Step 4: Simplify.

Example 5: Solve using the quadratic formula Step 1: Make sure it is in standard form. Step 2: Identify a, b, and c. a = 1 b = -2 c= -4

Example 5 (cont.) Step 3: Plug it into the formula….(don’t forget parentheses!)

Example 5 (cont.) Step 4: Simplify.

Example 6: Solve using the quadratic formula Step 1: Make sure it is in standard form. Step 2: Identify a, b, and c. a = 2 b = -7 c= 6

Example 6 (cont.) Step 3: Plug it into the formula….(don’t forget parentheses!)

Example 6 (cont.) Step 4: Simplify.

Assignment #46 Pg. 389 #1-14all