The Quadratic Formula and the Discriminant Algebra II Mr. Gilbert Chapter 6.5 The Quadratic Formula and the Discriminant Standard & Honors 1/13/2019

Agenda Warm up Homework Review Lesson New Homework Check your answers 1/13/2019

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Homework Review 1/13/2019

Example 1 Two Rational Roots (4) Example 2 One Rational Root (3) Example 3 Irrational Roots (4) Example 4 Complex Roots (5) Example 5 Describe Roots 1/13/2019 Lesson 5 Contents

Solve by using the Quadratic Formula. First, write the equation in the form and identify a, b, and c. 1/13/2019 Example 5-1a

Then, substitute these values into the Quadratic Formula. Replace a with 1, b with –8, and c with –33. Simplify. 1/13/2019 Example 5-1a

Answer: The solutions are 11 and –3. Simplify. Write as two equations. or Simplify. Answer: The solutions are 11 and –3. 1/13/2019 Example 5-1a

Solve by using the Quadratic Formula. Answer: 2, –15 1/13/2019 Example 5-1b

Solve by using the Quadratic Formula. Identify a, b, and c. Then, substitute these values into the Quadratic Formula. Quadratic Formula Replace a with 1, b with –34, and c with 289. Simplify. 1/13/2019 Example 5-2a

Answer: The solution is 17. Check A graph of the related function shows that there is one solution at 1/13/2019 Example 5-2a

Solve by using the Quadratic Formula. Answer: 11 1/13/2019 Example 5-2b

Solve by using the Quadratic Formula. Replace a with 1, b with –6, and c with 2. Simplify. 1/13/2019 Example 5-3a

or Answer: The exact solutions are and The approximate solutions are 0.4 and 5.6. 1/13/2019 Example 5-3a

Check. Check these results by graphing the related quadratic function, Check Check these results by graphing the related quadratic function, Using the ZERO function of a graphing calculator, the approximate zeros of the related function are –2.9 and 0.9. 1/13/2019 Example 5-3a

Solve by using the Quadratic Formula. Answer: or approximately 0.7 and 4.3 1/13/2019 Example 5-3b

Solve by using the Quadratic Formula. Write the equation in the form Now use the Quadratic Formula. Quadratic Formula Replace a with 1, b with –6, and c with 13. Simplify. 1/13/2019 Example 5-4a

Answer: The solutions are the complex numbers and Simplify. Answer: The solutions are the complex numbers and 1/13/2019 Example 5-4a

A graph of the function shows that the solutions are complex, but it cannot help you find them. 1/13/2019 Example 5-4a

Sum of a square; Distributive Property Check To check complex solutions, you must substitute them into the original equations. The check for is shown below. Original equation Sum of a square; Distributive Property Simplify. 1/13/2019 Example 5-4a

Solve by using the Quadratic Formula. Answer: 1/13/2019 Example 5-4b

Answer: The discriminant is 0, so there is one rational root. Find the value of the discriminant for . Then describe the number and type of roots for the equation. Answer: The discriminant is 0, so there is one rational root. 1/13/2019 Example 5-5a

Answer: The discriminant is negative, so there are two complex roots. Find the value of the discriminant for . Then describe the number and type of roots for the equation. Answer: The discriminant is negative, so there are two complex roots. 1/13/2019 Example 5-5a

Find the value of the discriminant for Find the value of the discriminant for . Then describe the number and type of roots for the equation. Answer: The discriminant is 80, which is not a perfect square. Therefore, there are two irrational roots. 1/13/2019 Example 5-5a

Find the value of the discriminant for Find the value of the discriminant for . Then describe the number and type of roots for the equation. Answer: The discriminant is 81, which is a perfect square. Therefore, there are two rational roots. 1/13/2019 Example 5-5a

Answer: 0; 1 rational root Find the value of the discriminant for each quadratic equation. Then describe the number and type of roots for the equation. a. b. c. d. Answer: 0; 1 rational root Answer: –24; 2 complex roots Answer: 5; 2 irrational roots Answer: 64; 2 rational roots 1/13/2019 Example 5-5b

Homework - Honors See Syllabus 6.5 Pg 318-319 15-39 multiples of 3, 40-45 1/13/2019

Homework See Syllabus 6.5 Pg 318-319 15-39 multiples of 3 1/13/2019