K-12 Grade 9 Math

04.26.2017

Module 1: Quadratic Equation and Inequalities
Lesson 1: Illustrations of Quadratic Equation

After going through this module, you should be able to demonstrate understanding of key concepts of quadratic equations, quadratic inequalities, and rational algebraic equations, formulate real-life problems involving these concepts, and solve these using a variety of strategies. Furthermore, you should be able to investigate mathematical relationships in various situations involving quadratic equations and quadratic inequalities.

Activity 1: Remember These?

Find the indicated product of each equation

3(x^2 + 7)	3x2 + 21
2s(s-4)	2s – 8s
(w+7)(w+3)	w2 + 7w +3w + 21	w2 + 10w + 21
(x+1)(x-2)	x2 – 2x + 9x – 18	x2 – 7x – 18

Activity 2: Another Kind of Equation

Below are different equations, identify whether the equations are linear or nonlinear.

• ·   2s + 3t = -7
• ·   6p – 9 = 10
• ·   8k – 3 = 12
• ·   3/4h + 6 = 0
• ·   C = 12n + 5

Activity 3: A Real Step to Quadratic Equation

Answer the situation below

     Mrs. Jacinto asked a carpenter to construct a rectangular bulletin board for her classroom. She told the carpenter that the board’s area must be 18 square feet.

A Quadratic Equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b, and c being constants, or numerical coefficients, and x is an unknown variable. One absolute rule is that the first constant “a” cannot be a zero.

Activity 4: Quadratic or Not?

Identify whether the expressions are quadratic. If not, then explain.

3m1 + 8 = 15	Not Quadratic	Highest Degree must be 2
x2- 5x + 10 = 0	Quadratic
12 + 4x = 0	Not Quadratic	Degree is missing
2t2 – 7t = 12	Quadratic
6 – 2x – 3x2 = 0	Quadratic

Activity 5: Does it Illustrate Me?

Identify whether the situations are quadratic or not

05.11.17

Module 1: Quadratic Equation and Inequalities

Lesson 2: Solving Quadratics by Extracting Square Roots

These knowledge and skills will help you in solving quadratic equations by extracting square roots.

Activity 1: Find my Roots!

Directions: Find the following square roots. Answer the questions that follow

Square root of -16	4
Square root of -25	-(5)
Square root of 49	7
Square root of -64	8i
Square root of 121	11
Square root of -289	-(17)
Square root of 0.16	0.4
Square root of +- 36	6i

Activity 2: What would make a statement true

Directions: Solve each of the following equations in as many ways as you can. Answer

x + 7 = 12	12 + (-7) = 5	x = 5
t – 4 = 10	(+4) + 10 = 14	t = 14
r + 5 = -3	(-5) + (-3) = -8	r = -8
x - 10 = -2	(+10) + (-2) = 8	x = 8
2s = 16	16 / 2*(s) = 8	s = 8
-5x = 35	35 / -5*(x) = 7	x = 7

Activity 3: Air Out

Directions: Use the situation below to answer the questions that follow.

Mr. Cayetano plans to install a new exhaust fan on his room’s square-shaped wall. He asked a carpenter to make a square opening on the wall where the exhaust fan will be installed. The square opening must have an area of 0.25 m2 .

How are you going to represent the length of a side of the square-shaped wall? How about its area?	Length = x2   Area = x
Suppose the area of the remaining part of the wall after the carpenter has made the square opening is 6 m2. What equation would describe the area of the remaining part of the wall?	x2 – 0.25 = 6