MATH 9

1. ILLUSTRATING
QUADRATIC
EQUATIONS
LESSON 1

2. ACTIVITY 1: Another Kind of Equation!
Below are different equations. Use these equations to answer the
questions that follow.
𝑥2
+ 5𝑥 + 3 = 0
2𝑠 + 3𝑟 = −7
8𝑘 − 3 = 12
9𝑟2
− 25 = 0
1
2
𝑥2
+ 3𝑥 = 8
4𝑚2
+ 4𝑚 + 1 = 0
𝑐 = 12𝑛 − 5
6𝑝 − 𝑞 = 10
𝑡2
− 7𝑡 + 6 = 0
9 − 4𝑥 = 15
𝑟2
= 144
3
4
ℎ + 6 = 0

3. ◦Which of the given equations are linear?
𝑥2
+ 5𝑥 + 3 = 0
2𝑠 + 3𝑟 = −7
8𝑘 − 3 = 12
9𝑟2
− 25 = 0
1
2
𝑥2
+ 3𝑥 = 8
4𝑚2
+ 4𝑚 + 1 = 0
𝑐 = 12𝑛 − 5
6𝑝 − 𝑞 = 10
𝑡2
− 7𝑡 + 6 = 0
9 − 4𝑥 = 15
𝑟2
= 144
3
4
ℎ + 6 = 0

4. ◦How do you describe linear equations?
𝑥2
+ 5𝑥 + 3 = 0
2𝑠 + 3𝑟 = −7
8𝑘 − 3 = 12
9𝑟2
− 25 = 0
1
2
𝑥2
+ 3𝑥 = 8
4𝑚2
+ 4𝑚 + 1 = 0
𝑐 = 12𝑛 − 5
6𝑝 − 𝑞 = 10
𝑡2
− 7𝑡 + 6 = 0
9 − 4𝑥 = 15
𝑟2
= 144
3
4
ℎ + 6 = 0

5. ◦How are these equations different from those which is linear?
𝑥2
+ 5𝑥 + 3 = 0
2𝑠 + 3𝑟 = −7
8𝑘 − 3 = 12
9𝑟2
− 25 = 0
1
2
𝑥2
+ 3𝑥 = 8
4𝑚2
+ 4𝑚 + 1 = 0
𝑐 = 12𝑛 − 5
6𝑝 − 𝑞 = 10
𝑡2
− 7𝑡 + 6 = 0
9 − 4𝑥 = 15
𝑟2
= 144
3
4
ℎ + 6 = 0

6. ◦What common characteristics do these equations have?
𝑥2
+ 5𝑥 + 3 = 0
2𝑠 + 3𝑟 = −7
8𝑘 − 3 = 12
9𝑟2
− 25 = 0
1
2
𝑥2
+ 3𝑥 = 8
4𝑚2
+ 4𝑚 + 1 = 0
𝑐 = 12𝑛 − 5
6𝑝 − 𝑞 = 10
𝑡2
− 7𝑡 + 6 = 0
9 − 4𝑥 = 15
𝑟2
= 144
3
4
ℎ + 6 = 0

7. Real Life Applications of Quadratic Equations
◦ https://www.youtube.com/watch?v=dGagFk1Baxk
◦ https://www.youtube.com/watch?v=ExpMqgwU0Ms

8. Quadratic Equation (In one variable )
◦is a mathematical sentence of degree 2 that can be
written in the following standard form. ax² + bx + c =
0, where a, b, & c are real numbers and a ≠ 0.

9. Parts of Quadratic Equations:
ax² + bx + c = 0
◦ax² - quadratic term
◦bx - linear tear
◦c - constant term

10. Example 1
2x² + 5x – 3 = 0 is a quadratic equation in
standard form
with a = _
b =_
c = _
2
5
-3

11. Example 2
3x(x – 2) = 10 is a quadratic equation. However, it
is not written in standard form.
3x(x – 2) = 10 → 3x² – 6x = 10
3x² – 6x – 10 = 10 – 10
3x² – 6x – 10 = 0
a = ____ b = _____ c = ______
3 -6 -10

12. Example 3
◦(2x + 5)(x – 1)
(2x + 5)(x – 1) = –6 → 2x² – 2x + 5x – 5 = –6
2x² + 3x – 5 = –6
2x² + 3x – 5 + 6 = –6 + 6
2x² + 3x + 1 = 0
a = _____ b = _____ c = _____
2 3 1

13. ACTIVITY 1
https://www.youtube.com/watch?v=plCeJ67UO4c&lis
t=PLPPsDIdbG32AaVkoigdocmIGY8F0nTViD