ME Math 9 Q1 0105sssssssssssssqas PS.pptx

quadratic formula

1. Lesson 1.5 Solving Quadratic Equations Using the Quadratic Formula

2. At the end of the lesson, the learners should be able to solve quadratic equations by: (a) extracting square roots; (b) factoring; (c) completing the square; and (d) using the quadratic formula.

3. At the end of the lesson, you should be able to correctly find the solution(s) to quadratic equations using the quadratic formula.

4. Have you watched an Olympic game or any athletic events like the javelin throw?

5. Javelin is a throwing event that makes use of a metal-tipped object being thrown as far as possible and would require a combination of power, strength, precision, and timing. When a javelin is thrown, its trajectory can be determined using a quadratic equation. The time it takes for a javelin to fall to the ground can also be computed using quadratic equations.

6. In the previous lesson, we learned how to solve quadratic equations by completing the square. In this lesson, we will explore more on solving quadratic equations using the quadratic formula.

7. How will you derive the quadratic formula using the method of completing the square for quadratic equations? How will you solve quadratic equations using the quadratic formula?

8. T his is the equation derived from the method of completing the square, which can be used for solving any quadratic equation. Quadratic Formula

9. Given the standard form of quadratic equation , the solutions of any quadratic equation are   Quadratic Formula

10. Example 1 : Find the solution(s) to using the quadratic formula.  

11. Example 1 : Find the solution(s) to using the quadratic formula.   Solution: Write the equation in standard form and identify the values of , , and .  

12. Example 1 : Find the solution(s) to using the quadratic formula.   Solution: Substitute the values of , , and to the quadratic formula. Then, simplify.  

13. Example 1 : Find the solution(s) to using the quadratic formula.   Solution:  

14. Example 1 : Find the solution(s) to using the quadratic formula.   Solution:  

15. Example 1 : Find the solution(s) to using the quadratic formula.   Solution: To determine the two solutions, we should separate the positive and negative signs. Thus, the solutions are and .  

16. Example 2 : Solve .  

17. Example 2 : Solve .   Solution: Write the equation in standard form and identify the values of , , and . The equation is already in standard form. Let us determine the values of , , and .  

18. Example 2 : Solve .   Solution: Substitute these values into the quadratic formula.  

19. Example 2 : Solve .   Solution: Substitute these values into the quadratic formula.  

20. Example 2 : Solve .   Solution: To determine the two solutions, we should separate the positive and negative signs. Thus, the solutions are and .  

21. Individual Practice: What are the solutions to the quadratic equation ? Use the quadratic formula to solve .  

22. Group Practice : Minimum of two groups to a maximum of five groups Erwin is four years younger than Sally. Find their present ages if the product of Sally’s age eleven years ago and Erwin’s age five years from now is 189.

23. A quadratic formula is an equation derived from the method of completing the square, which can be used for solving any quadratic equation. Given the standard form of quadratic equation the solutions of any quadratic equation can be solved as .  

24. Hansen, Mary. Master Math: Algebra 2. Boston, Massachusetts: Cengage Learning PTR, 2015. Purplemath . “Solving Quadratic Equations with the Quadratic Formula.” Accessed January 14, 2019. https://www.purplemath.com/modules/solvquad4.htm