1. Topic: The Parabola

2. The Graph of a quadratic function is a curve whose shape is called a parabola. Example : f(x) = 3x2

3. Points to Remember
The parabola generated by y = ax2 + bx + c opens Upward if a > 0 Downward if a < 0

4. Topic: Solving Quadratic Equations by Extracting the Square Root.

5. Key Concepts

6. Examples

8. Try this!
x2 = 49

9. Try this!
2x2 – 18 = 0

10. Try this!

11. Topic: Solving Quadratic Equations by Factoring.

12. Key Concepts. Zero Product Property For any real numbers x and y, if
xy = 0, then either x = 0 or y = 0 or both are equal to zero.
Examples:
x ( x + 3 ) = Ans. x = 0 and x = -3
(x-5) (x+3) = 0 Ans. x = 5 and x = -3
2. Procedures in Solving Quadratic Equation by Factoring. a.

13. Procedures in solving quadratic equations by Factoring.
Express the quadratic equation in the standard form ax2 + bx + c = 0.
Factor ax2 + bx + c as a product of linear factors.
Equate each linear factor to zero.
Solve each resulting equation.

14. Examples Solve x2 + 5x + 6 = 0 Solution: x2 + 5x + 6 = 0 Write in S.F
(x+2) (x+3)= Factor the left side
x + 2 = 0 and x+3 = 0 Set each factor
equal to zero
Answer: The solutions are -3 and -2

15. 3x( x – 7 ) = 0 Factor the left side 3x = 0 and x – 7 = 0
2. Find the roots of 3x2 – 21x = 0
Solution:
3x2 – 21x = 0 Write in S.F
3x( x – 7 ) = 0 Factor the left side
3x = 0 and x – 7 = 0
Therefore the roots are:
0 and 7

16. Try this!
x2 + 2x – 35 = 0

17. Try this!
x2 = x + 20

18. Try this!
3x2 + x = 0

19. Think-Pair-Share
Solve the following quadratic equations.
1. 7x2 – 28x = 0
2. 2b2 – 128 = 0
3. x2 = 196
4. y2 – 5y – 14 = 0
5. 3x2 + 2 = -7x

20. Board Drill
Solve the following quadratic equations.
x2 = 25

21. Board Drill
Solve the following quadratic equations. x2 – 64 = 0

22. Board Drill
x2 – 16 = 0

23. Board Drill
4x2 = 49

24. Board Drill
3x2 = 48

26. Board Drill
8x2 + x = 0

27. Board Drill
7x2 + 21x = 0

28. Board Drill
5x2 – x = 0

29. Board Drill
16x2 + 8x = 0

30. Board Drill
3x2 + 15x = 0

31. Board Drill
x2 – 6x + 8 = 0

32. Board Drill
x2 + 7x + 6 = 0

33. Board Drill
x2 – 5x + 6 = 0

34. Board Drill
x2 + 9x + 14 = 0

35. Board Drill
x2 – 8x + 15 = 0

36. Board Drill
x2 + 3x = 10

37. Board Drill
x2 = 7x + 18

38. Board Drill
4x2 + 4x + 1 = 0

39. Board Drill
14x2 + 17x + 5 = 0

40. Homework
Answer the problem. A vegetable garden measuring 30 feet by 20 feet has a walkway of uniform width around it. If the combined area of the garden and the walkway is 704 square feet; what is the width of the walkway?