Q1 WEEK 1 MATHEMATICS 9-Factoring & Completing the Square.pptx

Solving quadratic equations by factoring and completing the square

1. MATHEMATICS 9 WEEK 1 1ST QUARTER BY NOENIE N. EMBAJADOR

2. Circle Time Let's Gather in a Circle! Circle time is a special moment where we come together as a class family. We'll share questions and answer, discuss our plans for the day, and build a strong sense of community. Everyone's voice is important, so let's enjoy this time together!

3. story Time Luke sells digital cameras. He makes a total revenue of x 2 - 3000, where x is the number of cameras sold. However, the total production cost for the same number of cameras is 50x + 2000. To prevent losses, he should make and sell enough cameras to break even at the very least. How many cameras should Luke make and sell to break even?

4. story Time In sales, “break even” means no profit or loss is made. Since profit is the total revenue minus the total cost, you can represent Luke’s situation by the following equation: profit = total revenue - total cost 0 = (x 2 - 3000) - (50x + 2000) 0 = x 2 - 3000 - 50x - 2000 0 = x 2 -50x - 5000 Since x represents the number of cameras, you have to solve for x in the equation x 2 - 50x - 5000 = 0. How will you now solve for x?

5. quadratic equations Objectives: -illustrates quadratic equations -solves quadratic equations by: completing the square and factoring

6. quadratic. equations A quadratic equation is a second-degree polynomial equation. It is written in standard form as ax 2 + bx + c = 0 for any real numbers a, b, and c, where a = 0.

7. x 2 + 2x - 15 4x 2 - 20x + 25 x (2x + 9) - 11 EXAMPLES OF QUADRATIC EQUATIONS:

8. solving quadratic equations by Factoring

9. examples: A. x 2 – 7x + 10 = -2 B. x 2 + 2x + 1 = 0

10. examples: x 2 + 2x – 15 4x 2 – 20x + 25 x(2x + 9) – 11 x 2 – 3 = 2x

11. Check-up quiz: 2 (x 2 + 2) = -9x 3x 2 + 5x = 0 x 2 – 3 = 2x (x + 2) (x + 3) = 12 10x – 6(x-1) – x (x-1)

12. solving quadratic equations by Completing the Square

13. examples: A. x 2 + 22x + 21 = 0 B. x 2 - 4x + 2 = 0 C. 2x 2 - 4x + 1 = 0

14. Activity No. 1: Solve each quadratic equation by factoring. Show your solution. x 2 + 6x + 8 = 0 x 2 + 6x = 12 2x 2 – x – 6 = 0

15. Activity No. 2: Solve each quadratic equation by completing the square. Show your solution. Using the square tiles: x 2 + 6x + 3 = 0 Traditional solving: 3x 2 + 4x - 5 = 0

16. thank you! Should you have any questions?