Math_grade_9_q1_-module1l1_-illustrates-quadratic-equations.pdf

Republic of the Philippines

Department of Education Region III – Central Luzon Schools Division of Pampanga

DONNA MARIE D. TONGOL SSt-Iii Writer JANE P. VALENCIA , EdD

EPS I - MATHEMATICS

Avengers: The Six Infinity Stones

TITLE :

LESSON 1: ILLUSTRATION OF QUADRATIC EQUATIONS

GUIDE CARD

Learning Competency: Illustrate quadratic equations. M9AL-Ia-1

Thanos is one of the greatest villains in the Marvel movie. His primary quest has been self –serving, full of evil, and is always based on collecting the Infinity Stones to make him the most powerful being in the universe. He has made Power…but he really wants ALL the Powers! In order to defeat Thanos, the Avengers, Guardians of the Galaxy, really need to find out how a particular quadratic equation is illustrated in real-life by taking his INFINITY STONES out of the vault and secure them himself. Before doing the activities, read and understand first some important notes on QUADRATIC EQUATIONS and examples presented.

We know that a quadratic polynomial can be written as ax2 + bx + c. If the quadratic polynomial = 0, it forms a quadratic equation. Therefore, the standard form of a quadratic equation can be written as: ax2 + bx + c = 0 ; where x is an unknown variable, and a, b, c are constants with ‘a’ ≠ 0 (if a = 0, then it becomes a linear equation). The constants ‘a’, ‘b’ and ‘c’ are called the coefficients.

In the quadratic equation, ax2 is the quadratic term , bx is the linear term, and c is the constant term. Let us look at some examples of a quadratic equation: 

2x2+5x+3=0;

In this, a=2, b=5 and c=3



x2-3x=0; not

Here, a=1 since it is 1 times x2, b=-3 and c=0, shown as it is zero.



Ok got it! Let us now represent each situation by mathematical statement. Identify the situation that can be represented by quadratic equation. First, I’ll be giving example:  The area of a rectangular lot is 860m 2. The length is 3 more than twice the width. Represent the quadratic equation. First, let us represent width (w)= x length (l) = 2x+3 The area of a rectangle is A=l · w Therefore, substituting the formula. 860=x(2x+3) 860= 2x2+3x 2x2+3x-860=0 where a=2, b=3, c=-860

Let us try more examples for us to get the stones from Thanos! Numbers 1-4 is done for you.

Equation 1. x2 – 3x = 1

Standard Form x2 – 3x – 1 = 0

Coefficients a= 1, b= -3, c=-1

Explanation Compare it to the general form of the quadratic equation and subtract 1 from both sides.

2.2(z2 – 2z)=5

2z2-4z-5 =0

3.y(y-2)=0

4. -x2 =4 -9x

a= 2, b= -4, c=-5

y2-2y=0

a=1, b=-2 ,c=0

-x2 +9x -4 =0

a=-1, b=9, c = -4

We need to expand (open the brackets) by multiplying 2 with z2 and -2z and also we need to bring 5 to the left side to equate the equation with 0. We need to expand, multiply y with both y and -2 and the output you get is in the desired standard form. We need to eliminate 4 and -9x to the right side to equate the equation with 0.

Activity Card ACTIVITY 1. COMPLETE ME! Complete the table. Equation 1.12-4x +2x2=7 2. 3c(2c +2) =9 3.(b+2)(b-3)=10 4. (x+4) (x-5) =0 5. 6x2 -5 =7x

Standard Form

Coefficients

ACTIVITY 2. Set My Standard as Easy as abc! Write each quadratic equation in standard form, ax²+bx+c=0 then identify the values of a, b, and c. Quadratic Equation

Standard Form

a

b

(x+5)(x+5)=3 (2x-3)²=-5 3(x+5)²-5=0 2(4x+2)²=2x+1 (x+6)(3x-2)=5+2x

ACTIVITY 3. My Situation! My Equation! Illustrate the following situations in quadratic equations.

My Situation! 1. The length of the window is 2m longer than its width and the area is 32m². 2. A square garden will be planted by a border of flowers. The border will be of the same dimensions around the entire garden which has an area of 73m². 3. The width of the blackboard in Sir Red’s room is 4 less than its width. The blackboard has an area of 40m². 4. The entrance door in Math room has a width is greater than 8 than its length. What is equation in finding the area of the door? 5. A ball is thrown straight up, from 3 m above the ground, with a velocity of 14 m/s. Add them up and the height h at any time t is: h = 3 + 14t - 5t²

My Equation!

c

Assessment Card Multiple Choice. Choose the letter of the correct answer. Write the chosen letter on space before each number. ___1. Which of the following is a quadratic equation? A. x – 6x + 10 = 0 C. 2x – 3x – 9 = 0 B. (x – 1) = 0 D. (x + 1) (x – 2) = 0 ___2. Which of the given is a quadratic term? A. 6x B.8x² C.– 9 D. 5xᶾ ___3. The following are examples of quadratic equation EXCEPT: A. x²+ x - 2 = 0 C. (x + 5)2 = 0 B. (x – 2) (x + 4) = 0 D. (x² – 3) (x +2) = 0 ___4. Which of the following is equal to (x -4) (x - 6) = 2? A.x² – 10x +22 = 0 C. x² – 10x -22 = 0 B.x² + 10x –22 = 0 D. x² + 10x +22 = 0 ___5. What is the standard form of the equation 2x² -4x + 5/3=(x-1)(x+2)/2? A.9x² – 21x - 16 = 0 C. 9x² + 21x + 16 = 0 B.9x² - 21x + 16 = 0 D. 9x² + 21x – 16 = 0 ___6. What is the standard form of (x+5)²=3? A.x²+10x+22=0 C.x²+10x+25=0 B. x²+25x-3=0 D. 5x²+10x-3=0 ___7. What is the constant term in the quadratic equation x(x+6) = 7? A. x² B. 6x C. 7 D.-7 ___8. (x+5)² + (x – 2)² = 37 can also be written as ___________________. A. 2x2 +6X -8= 0 C. 2x2 + 30x – 48 = 0 B. 2x2 -6X +8= 0 D. 2x2 – 48x + 30 = 0 ___ 9. A rectangular table has an area of 40 ft2 and a perimeter of 28 ft. Represent the area of the rectangular table. A. A= 40ft2 C. 40 = s2 B. 40ft2 = l· w D. none of the above ___ 10. The entrance door in Math Laboratory has a width is greater than 7 than its length. What is equation in finding the area of the door? A. ( x) (x+7) = A C. (w) (l+7) = A B. (x) (x-7 ) = A D. (w) ( L -7) =A

Enrichment Card

Congratulations! You did great! Now let us try more activities, for you to get one stone, answer the activity correctly.

A. Identify which of the following equations are quadratic, and which are not. Write Q if the equation is quadratic and NQ if not and explain. Use an extra sheet of paper for your explanation. ______1. x2 =9 ______ 2. y(y-6) =10 ______3. 6x+9y =2 ______4. 1+4x2 = 4 2 ______ 5. 1 - 2b = 12 2

____6. 3x=9 ____ 7. √2x- 4= 4 ____ 8. 6m = m 2 -27 ____ 9. 5y-10 = y2 √𝑦 − 1 ____ 10. a+b –c=0

B. Write each quadratic equation in standard form ax2 + b x + c =0 then identify the values of a, b, and c. Answer the questions that follow. 1. 2. 3. 4. 5.

3 + x +x2 = 2 –x2 m (3m -4m +5)=6 4- 6x2=10 ( 2a + 1)2+4=0 3c( c- 2) -2= 12

STANDARD FORM _________________ _________________ _________________ _________________ _________________

a, b, c ___, ____, _____ ___, _____, _____ ___, _____, _____ ___, _____, _____ ___, _____, _____

Let us try another activity for us to defeat Thanos. Let ‘s go!

There are verbal mathematical statements below. Let us identify the situation that can be represented by quadratic equation.

C.MATCH IT TO ME There are verbal statements below. Look for the mathematical expression or quadratic equation in the figures that correspond to each verbal statement. 1. The product of two consecutive positive integers is 240. 2. Mr. Valencia wants to build a rectangular pen for his goats. What is the biggest possible area he can enclose with 40 meters of fencing? 3. Mark traveled from Pampanga to Manila, a distance of 120km. He found out that by increasing his speed by 20 kph, he can travel the same distance an hour less. 4. Find two numbers whose sum is 14 such that the sum of their squares is a minimum value. 5. Mike 3 hours more to do a piece of work than Ian. They together complete it in 2 hours.

S= (14-x)2+x2

x2-2x=240

A= 20x-x2

x(x+1)=6

S=196-28x+2x2

x2-20x+100=0 x2+x=240

x2-x-6=0

Great Job! Excellent

ACTIVITY 1 1. 2. 3. 4. 5.

2x2 -4x + 5 =0 6c2 + 6c -9 =0 b2 - b -6 =0 x2 - x -20 =0 6x2 -7 x -5 =0

ACTIVITY 2 a=2, b=-4 ,c=5

Standard Form

a=6, b=6, c= -9

b

c

x2 +10x + 22=0

1

10

22

4x2 -12x + 14=0

4

-12

14

3x2 +30x + 70=0

3

30

70

32x2 +30x + 7=0

32

30

7

3x2 +14x -17=0

3

14

-17

a=1, b=-1, c= -6 a=1, b=-1, c= -20 a=6, b=-7, c= -5

ACTIVITY 3

1. A= lw 32m²=w(w+2) 0=w²+2w-32 2.A= s² 81m²=s² 0=s²-81 3. A=40m² w=l-4 A=lw 40m²=l(l-4) 0=l²-4l-40 4. A= lw width=x+8 length=x A=x(x+8) A= x²+8 5.-5t² + 14t + 3 = 0

a

ENRICHMENT CARD A. 1. Q

6. NQ

2. Q

7. NQ

3. NQ

8. Q

4. Q

9. NQ

5. NQ

10. NQ

B. 1. 2x2 +x + 1 =0 2. -m2 +5m -6 =0

3. 6x2 -6 =0 4. 4a2 +4a + 5 =0 5. 3c2 -6c -14 =0

Bryant, Merden L. ,Bulalalyao, Leonides E. , Callanta , Melvin M. , Cruz , Jerry D. , De Vera, Richard F. , Garcia, Gilda T. , Javier , Sonia E. , Lazaro , Roselle A., Mesterio, Bernadette J. , and Saladino Rommel Hero A., Mathematics Grade 9 Learner’ Materials, First Edition ,pp.66. Tizon, Lydia and Ulpina , Jisela Naz, JO-ES Publishing House , Math Builders 2007, Valenzuela City , pp. 70-96 Math-Only-Math.2010-2020.http://www.math-only-math.com/solving quadratic-equations.html Purple Math. Solving Quadratic Equations by taking Square Roots. 2020 http://www.Purplemath.com/modules/solvquad2.html