QUADRATIC EQUATIONS INVOLVING COMPLETING THE SQUARE.ppt
- 1. California Standards 14.0 Students solve a quadratic equation by factoring or completing the square.
- 2. Objective: Objective: We will solve quadratic We will solve quadratic equations by completing equations by completing the square. the square. Pair share non-volunteer
- 3. APK Simplify. Teacher does 1 Students do 2,3,4 1. 2. 3. 4. This is how you find the end term of completing the square
- 4. Solving by completing the square is adding a term to x2 + bx to form a trinomial that is a perfect square. Choral read- pairshare ā in own words Concept development
- 5. X2 +10x +25 Example x2 ā8x +16 Non -example ā¬ x2 ā25 When completing the square the expression needs to be in standard form ā¬ ax2 +bx +c ā¬ x3 +5x +10 Which one is an example of a completed square? X2 +15 X2 ā20x +100 A. B. Justify
- 6. 9-7 Completing the Square Importance: Importance: 1. Landscapers can solve quadratic equations to find dimensions of patios. 2. Itās on the chapter, benchmark, and CST tests.
- 7. Additional Example 1: Completing the Square Complete the square to form a perfect square trinomial. A. x2 + 2x + B. x2 ā 6x + x2 + 2x x2 + 2x + 1 Identify b. . I do We do How did I/we complete the square to form a perfect square trinomial?
- 8. Guided Practice (You do) Complete the square to form a perfect square trinomial. c. 8x + x2 + Identify b. . How did you find the perfect square trinomial?
- 9. Additional guided practice (if needed) Complete the square to form a perfect square trinomial. a. x2 + 12x + b. x2 ā 5x + Identify b. .
- 10. To solve a quadratic equation in the form x2 + bx = c, first complete the square of x2 + bx. Then you can solve using square roots. Concept Development How do you solve a quadratic equation x2 + bx = c?
- 11. Solving a Quadratic Equation by Completing the Square Skill development
- 12. Completing the Square (I do) Solve by completing the square. Check your answer. x2 + 16x = ā15 Step 1 x2 + 16x = ā15 Step 2 Step 3 x2 + 16x + 64 = ā15 + 64 Step 4 (x + 8)2 = 49 Step 5 x + 8 = Ā± 7 Step 6 x + 8 = 7 or x + 8 = ā7 x = ā1 or x = ā15 The equation is in the form x2 + bx = c. Complete the square. Factor and simplify. Take the square root of both sides. Write and solve two equations. . Why? How?
- 13. Guided Practice (we do) Solve by completing the square. Check your answer. x2 + 10x = ā9 Step 1 x2 + 10x = ā9 Step 3 x2 + 10x + 25 = ā9 + 25 Complete the square. The equation is in the form x2 + bx = c. Step 2 Step 4 (x + 5)2 = 16 Step 5 x + 5 = Ā± 4 Step 6 x + 5 = 4 or x + 5 = ā4 x = ā1 or x = ā9 Factor and simplify. Take the square root of both sides. Write and solve two equations. . How did we?
- 14. You Do x2 +8x = 9 Step 1 Step 2 Step 3 Step 4 Step 5 Step 6
- 15. Additional Guided practice (If needed) Solve by completing the square. Check your answer. x2 ā 4x ā 6 = 0 Write in the form x2 + bx = c. Complete the square. Factor and simplify. Take the square root of both sides. Write and solve two equations. .
- 16. Additional Guided Practice (if needed) t2 ā 8t ā 5 = 0 Complete the square. Write in the form x2 + bx = c. Factor and simplify. Take the square root of both sides. Write and solve two equations. . Solve by completing the square. Check your answer.
- 17. I do (simplifying first) Solve by completing the square. ā3x2 + 12x ā 15 = 0 .
- 18. Guided practice (we do) Solve by completing the square. 2t2 + 5t = 3
- 19. Guided practice (we do) Solve by completing the square. 2x2 = -7x - 29
- 20. Guided practice (we do) Solve by completing the square. 4t2 ā 4t + 9 = 0
- 21. Complete the square to form a perfect square trinomial. 1. x2 + 11x + 2. x2 ā 18x + Solve by completing the square. 3. x2 ā 2x ā 1 = 0 4. 3x2 + 6x = 144 5. 4x2 + 44x = 23 Closure Skill (Every variation)
- 22. 9-7 Completing the Square Closure Closure 1. What is the process of adding to x2 + bx called? 2. What did you learn about solving a quadratic equation by completing the square? Why is this important to learn? ā¬ b 2 ā ā ā ā ā ā 2
- 23. 9-7 Completing the Square Independent practice Independent practice ļ Practice book pg 62 1-6