This document provides examples and explanations of linear and quadratic equations. It discusses the standard form of quadratic equations (ax^2 + bx + c = 0) and provides examples of identifying the a, b, and c coefficients of various quadratic equations. It also contains practice problems asking students to determine if equations are quadratic and if so, identify the a, b, and c values.

1. Illustrating
Quadratic Equation

2. An equation of the first degree in any number of
variables.
LINEAR EQUATION
𝑥 + 𝑦 = 8

3. QUADRATIC EQUATION
𝑥2
− 3𝑥 + 15 = 0
Aseconddegreeequation.
Thehighestexponentofthevariableis2

4. Which of these are quadratic equations?
𝑥2
− 10𝑥 + 3 = 0
7𝑥3
+ 4𝑥 = 0
𝑥2 − 𝑥5 + 25 = 𝑥
𝑦7 = 𝑦2
8𝑥 = 10𝑥2
𝑥 + 2 = 11𝑥2
𝑥 − 2 𝑥 + 1 = 3
2𝑥 𝑥 − 5 = −1
4𝑥 𝑥2 + 9 = 3
9𝑚 − 𝑚2
= 11

6. 𝑥2
− 3𝑥 + 15 = 0
𝑥2 −3𝑥 15
𝑎 = 1 𝑏 = −3 𝑐 = 15

7. 2𝑥2
+ 6𝑥 − 10 = 0
2𝑥2 6𝑥 −10
𝑎 = 2 𝑏 = 6 𝑐 = −10

8. 5𝑥2
− 𝑥 − 8 = 0
5𝑥2 −𝑥 −8
𝑎 = 5 𝑏 = −1 𝑐 = −8

9. Determine if the given equation is quadratic. If yes, identify the
values of a, b, and c.
𝑥2
− 10𝑥 − 3 = 0
Standard form
𝑎𝑥2
+ 𝑏𝑥 + 𝑐 = 0
𝑎 = 1 𝑏 = −10 𝑐 = −3

10. Determine if the given equation is quadratic. If yes, identify the
values of a, b, and c.
8𝑥2
− 𝑥 + 2 = 0
𝑎𝑥2
+ 𝑏𝑥 + 𝑐 = 0

11. Determine if the given equation is quadratic. If yes, identify the
values of a, b, and c.
3𝑥2
+ 5𝑥 = 10
𝑎𝑥2
+ 𝑏𝑥 + 𝑐 = 0

12. Determine if the given equation is quadratic. If yes, identify the
values of a, b, and c.
25𝑥2
− 2𝑥 = −8
𝑎𝑥2
+ 𝑏𝑥 + 𝑐 = 0

13. Determine if the given equation is quadratic. If yes, identify the
values of a, b, and c.
4𝑥 + 6𝑥2
= 3
𝑎𝑥2
+ 𝑏𝑥 + 𝑐 = 0

14. Determine if the given equation is quadratic. If yes, identify the
values of a, b, and c.
7𝑥2
+ 11 = 0

15. Determine if the given equation is quadratic. If yes, identify the
values of a, b, and c.
6𝑥 + 2𝑥2
= 0

16. Activity No. 1
Identify the values of a, b, and c.
1. 6𝑥 + 2𝑥2
= 0
2. 𝑥2
−6𝑥 = 1
3. 2𝑥2
= −12
4. 7𝑥2
+ 𝑥 = 3
5. 13𝑥2
− 2 = 0

17. Activity No. 2
Identify the values of a, b, and c.
1. 4𝑥2
− 9𝑥 = 5
2. 𝑥 + 8𝑥2
= 0
3. 21𝑥2
= 13
4. 𝑥2
= −4𝑥 + 10
5. 11𝑥2
− 𝑥 − 1 = 0

18. Determine if the given equation is quadratic. If yes, identify the
values of a, b, and c.
𝑥 = 3 + 𝑦

19. Determine if the given equation is quadratic. If yes, identify the
values of a, b, and c.
6𝑥3
− 𝑥2
+ 25 = 0

20. Determine if the given equation is quadratic. If yes, identify the
values of a, b, and c.
ACTIVITY NO. 1 (9-Silver)
1. 𝑥2
− 6𝑥 + 2 = 0
2. 3𝑥 + 5 = 0
3. 2𝑥2
+ 7𝑥 = 15
4. 𝑥2
= 7𝑥 + 8
5. 4𝑥2
− 𝑥 + 3 = 0
6. 6𝑥 + 𝑥2
= 12
7. 9 = 7𝑥2
8. 7𝑥2
+ 4 = 0
9. 𝑥 − 14 = 0
10. 3𝑥2
+ 6 = 𝑥8

23. Determine if the given equation is quadratic. If yes, identify the
values of a, b, and c.
HOMEWORK NO. 1 (9-Gold)
1. 𝑥2
− 6𝑥 + 2 = 0
2. 3𝑥 + 5 = 0
3. 2𝑥2
+ 7𝑥 = 15
4. 𝑥2
= 7𝑥 + 8
5. 7𝑥2
= 10
6. 𝑥 − 1 𝑥 + 2 = 𝑥
7. 3𝑥 4𝑥 + 1 = 18
8. 𝑥 𝑥2
− 2 = 5𝑥 + 1
9. 5𝑥2
− 𝑥 = 0
10. 𝑥 + 5 2
= −1

24. 4𝑥2
= 20
4𝑥2
− 20 = 0
𝑎 = 4 𝑏 = 0 𝑐 = −20

25. 2𝑥 = −5𝑥2
5𝑥2
+ 2𝑥 = 0
𝑎 = 5 𝑏 = 2 𝑐 = 0

26. 4𝑥2
+ 𝑥 = 𝑥 − 1 2
4𝑥2
+ 𝑥 = (𝑥 − 1)(𝑥 − 1)
4𝑥2
+ 𝑥 = 𝑥2
− 𝑥 − 𝑥 + 1
4𝑥2
+ 𝑥 − 𝑥2
+ 𝑥 + 𝑥 − 1 = 0
3𝑥2
+ 3𝑥 − 1 = 0
𝑎 = 3 𝑏 = 3 𝑐 = −1

27. 2𝑥 + 5 𝑥 + 1 = 8
2𝑥2
+ 2𝑥 + 5𝑥 + 5 = 8
2𝑥2
+ 7𝑥 + 5 − 8 = 0
2𝑥2
+ 7𝑥 − 3 = 0
𝑎 = 2 𝑏 = 7 𝑐 = −3

28. 5𝑥 𝑥 − 9 = 12
5𝑥2
− 45𝑥 = 12
5𝑥2
− 45𝑥 − 12 = 0
𝑎 = 5 𝑏 = −45 𝑐 = −12

29. 𝑥 + 9 2
= 3𝑥
𝑥 + 9 𝑥 + 9 = 3𝑥
𝑥2
+ 9𝑥 + 9𝑥 + 81 = 3𝑥
𝑎 = 1 𝑏 = 15 𝑐 = 81
𝑥2
+ 18𝑥 + 81 − 3𝑥 = 0
𝑥2
+ 15𝑥 + 81 = 0

30. 7𝑥 = −3𝑥2
3𝑥2
+ 7𝑥 = 0
𝑎 = 3 𝑏 = 7 𝑐 = 0

31. ACTIVITY NO. 2
Complete the table below.
Standard
Form
a b C
1. 8𝑥 = −9𝑥2
2. 6𝑥 𝑥 − 1 = 6
3. 𝑥 + 7 2 = 12𝑥