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1. 9-9 The Quadratic Formula and the Discriminant Holt Algebra 1

2. Thursday, March 28, 2019 • Bell Ringer • Evaluate each when a = - 3 , b = 2, and c = 1. • b2 – 4ac • abc – a2 • Solve 8x2 – 13x – 6 = 0, using the Quadratic Formula.

3. Thursday, March 28, 2019 • STANDARD: A.REI4b • Learning Objectives: S.W.B.A.T.: • Solve quadratic equation by using the Quadratic Formula • Determine the number of solutions of a quadratic equation using the discriminant. • Essential Question: • How can a quadratic equation that is not factorable be solved?

7. b2 – 4ac is zero. b2 – 4ac is negative. b2 – 4ac is positive. There are two real solutions There is one real solution There are no real solutions Example 3: Using the Discriminant Find the number of solutions of each equation using the discriminant. A. B. C. 2x2 + 11x + 12 = 0 3x2 – 2x + 2 = 0 x2 + 8x + 16 = 0 a = 2, b = 11, c = 12 a = 3, b = –2, c = 2 a = 1, b = 8, c = 16 b2 – 4ac b2 – 4ac b2 – 4ac (–2)2 – 4(3)(2) 112 – 4(2)(12) 82 – 4(1)(16) 4 – 24 121 – 96 64 – 64 –20 25 0

8. Seatwork • Find the number of solutions of each equation using the discriminant. • 2x2 – 2x + 3 = 0 • x2 + 4x + 4 = 0 • x2 – 9x + 4 = 0

11. Solution:

12. Seatwork 2.

13. Assignment 6. Answer all even numbers from 14 to 28, page 587 of the textbook.

15. Example 5: Solving Using Different Methods Solve x2 – 9x + 20 = 0. Show your work. Method 1 Solve by graphing. Write the related quadratic function and graph it. y = x2 – 9x + 20 The solutions are the x-intercepts, 4 and 5.

17. VOCABULARY Discriminant

20. Example 5 Continued Solve x2 – 9x + 20 = 0. Show your work. Method 2 Solve by factoring. x2 – 9x + 20 = 0 (x – 5)(x – 4) = 0 Factor. Use the Zero Product Property. x – 5 = 0 or x – 4 = 0 x = 5 or x = 4 Solve each equation.

21. Add to both sides. x2 – 9x + = –20 + Example 5 Continued Solve x2 – 9x + 20 = 0. Show your work. Method 3 Solve by completing the square. x2 – 9x + 20 = 0 x2 – 9x = –20 Factor and simplify. Take the square root of both sides.

22. Example 1: Using the Quadratic Formula Solve using the Quadratic Formula. A. 6x2 + 5x – 4 = 0 B. x2 = x + 20 C. 3x2 – 2 x = 5

24. Example 5 Continued Solve x2 – 9x + 20 = 0. Show your work. Method 3 Solve by completing the square. Solve each equation. x = 5 or x = 4

25. Example 5: Solving Using Different Methods. Solve x2 – 9x + 20 = 0. Show your work. Method 4 Solve using the Quadratic Formula. 1x2 – 9x + 20 = 0 Identify a, b, c. Substitute 1 for a, –9 for b, and 20 for c. Simplify. Write as two equations. x = 5 or x = 4 Solve each equation.

26. Lesson Quiz: Part I 1. Solve –3x2 + 5x = 1 by using the Quadratic Formula. 2. Find the number of solutions of 5x2 – 10x – 8 = 0 by using the discriminant. ≈ 0.23, ≈ 1.43 2

27. Lesson Quiz: Part II 3. The height h in feet of an object shot straight up is modeled by h = –16t2 + vt + c, where c is the beginning height of the object above the ground. An object is shot up from 4 feet off the ground with an initial velocity of 48 feet per second. Will it reach a height of 40 feet? Use the discriminant to explain your answer. The discriminant is zero. The object will reach its maximum height of 40 feet once. 4. Solve 8x2 – 13x – 6 = 0. Show your work.

28. Warm-Up 1. Solve –3x2 + 5x = 1 by using the Quadratic Formula. 2. Find the number of solutions of 5x2 – 10x – 8 = 0 by using the discriminant. ≈ 0.23, ≈ 1.43 2

29. Wednesday, March 27, 2019 Bell Ringer Evaluate for x =–2, y = 3, and z = –1. 1. x2 4 2. xyz 6 3. x2 – yz 4. y – xz 7 1

31. Independent Practice: (To be turned – in by the end of the period) • Solve using the quadratic formula. • x2 + 2x – 35 = 0 • 3x2 + 7x + 2 = 0 • x2 + x – 20 = 0 • 2x2 – 9x – 5 = 0