Solving Quadratic Equation

1. 9

3. Checking of Attendance

11. It’s Good to be Simple!
Simplify the expression.
=
8
2
4

12. It’s Good to be Simple!
Simplify the expression.
=
2
6
1
3

13. Hi! I’m
Phineas.
and
I’m
Ferb!
We’re
brothers...
Are you ready
for our
Mathematics
Adventure?
Yes…
Our first task
is to find out
what is inside
this box?

14. Q
u a d
r
a b
For us to
find what is
inside the
box
Let’s play
PictoWord!
Ok, I’m
so
excited!
Guess our
first word!
Great! Our
first word is
Quadratic.
a
t i
c
- nt - sk

15. e r f m p o
Now guess
the second
word…
Great! Our
second
word is
line!
a
l
u
- u - sic - p

16. QUADRATIC
FORMULA
So today’s
adventure is all
about “Solving
quadratic equation
using quadratic
formula”
Now let
us see
what’s
inside the
box!

17. Isabella is
missing…
We have to
find her!
Will you help
us find her?
That’s
Great! Thank
you

18. But where are
we going to
start?
We need
something
like…
map
Right!
Oh thank you
perry!
We’ll gonna
pass the
theme park
enter dark
forest..
Isabella is
here on
this island
Then cross
the river…
We’re
here…
And find
Isabella..

19. Let’s go!

21. Theme Park is under
renovation! You can
use this alternative
route.
What is
this?

22. Right! A roller
coaster.

23. It’s a roller
coaster!
You have to ride with us so we
can go through!
𝑦 = 𝒙𝟐
− 𝒙 − 𝟐

25. What energy is applied in riding
a roller coaster?
Gravitational Potential Energy and
Kinetic Energy

26. On a roller coaster, energy changes from potential
to kinetic energy and back again many times over
the course of a ride.

27. And where do
you think
you’re going?!
Oh, Candice, please let us pass. We have to
find Isabella!
Oops, I'm
sorry, but I
need your help
to solve this
first.
What could it be? Let us help Candice.

28. Help me find the solutions of each of the following
quadratic equations using the quadratic formula.

29. To solve any quadratic equation using quadratic formula,
the following procedure can be followed.
Transform the quadratic equation into standard
form, if necessary.
STEP
1
STEP
2
Determine the values of a, b and c.
STEP
3
Substitute the value of a, b and c in the
equation 𝒙 =
−𝒃 ± 𝒃𝟐−𝟒𝒂𝒄
𝟐𝒂
STEP
4
Simplify the result.
STEP
5
Check the solutions obtained by substituting
each in the original equation.

30. This is the
rubrics for your
performance in
doing the task.
Category 5 3 1
Participation If all the students
participate in the
activity
If there are only few
students did not
participate in the activity
Most of the students
did not participate in
the activity
Cleanliness &
Design
No erasure with
design
Less erasure with design Too many erasure with
design
Correctness &
Presentation
With complete
correct answer
With incomplete answer Without correct
answer
Time Finished the task on
time
Finished the activity after
the given time
Did not finished the
activity
Participation If all the students
participate in the
activity
If there are only few
students did not
participateintheactivity
Most of the students
did not participate in
theactivity
Cleanliness &
Design
No erasure with
design
Lesserasure withdesign Too many erasure with
design
Correctness &
Presentation
With complete
correct answer
With incompleteanswer Without correct
answer
Time Finished the task on
time
Finished the activity after
thegiventime
Did not finished the
activity
5
10
15

31. 5 minutes
End
You only have 5
minutes to
finish your
task.

32. This is the
rubrics for your
performance in
doing the task.
Category 5 3 1
Participation If all the students
participate in the
activity
If there are only few
students did not
participate in the activity
Most of the students
did not participate in
the activity
Cleanliness &
Design
No erasure with
design
Less erasure with design Too many erasure with
design
Correctness &
Presentation
With complete
correct answer
With incomplete answer Without correct
answer
Time Finished the task on
time
Finished the activity after
the given time
Did not finished the
activity
Participation If all the students
participate in the
activity
If there are only few
students did not
participateintheactivity
Most of the students
did not participate in
theactivity
Cleanliness &
Design
No erasure with
design
Lesserasure withdesign Too many erasure with
design
Correctness &
Presentation
With complete
correct answer
With incompleteanswer Without correct
answer
Time Finished the task on
time
Finished the activity after
thegiventime
Did not finished the
activity
5
10
15

33. How did you use the quadratic
formula in finding the solution/s
of each equation?
Was it easy for you to find the
solutions of quadratic equation
using the quadratic formula?
What is quadratic formula?
Did you find the solution/s of
quadratic equation?
What did you use to solve the
quadratic equations?
Now you
have to
clear
your
way!
Well
done!

34. Let see if we
got
everything
right!
Great! Let’s
keep going!

36. Hey! What brings
you here in my
forest?!
Oh, Mr. We need to pass through your forest
to find our friend.
That won’t do,
this forest has
many traps, make
your way safely!
What was that, the ground is shaking!

37. I will let you pass if
you can enumerate
the STEPS in
SOLVING
QUADRATIC
EQUATION using
QUADRATIC
FORMULLA
Do you
know who
am I?!
I am a
giant hill
with
beautiful
parabola!

38. Check the solutions obtained
by substituting each in the
original equation.
Simplify the result.
Substitute the value of a,
b and c in the equation
𝒙 =
−𝒃 ± 𝒃𝟐−𝟒𝒂𝒄
𝟐𝒂
Determine the values
of a, b and c.
Transform the quadratic
equation into standard form,
if necessary.
Great! We
had
cleared the
way…

40. Woah! There’s
a big wave
coming
Hurry, let's
find the
solutions so it
won't crash
into our boat!
Use quadratic formula to
find the solutions of the
given quadratic equations.

41. What Must be My length and Width?
“The municipality of Tanay is preparing the municipal
hall for the Tanay Hane Festival, scheduled for
November 11-13, 2023. As part of the preparations, a
group of students has been assigned the task of
decorating the exterior wall of the municipal hall with
recycled decorations. To accomplish this task, they
need to determine the length and width of the
municipal hall. The quadratic equation given describes
the estimated area of Municipal Hall of Tanay is
𝒙𝟐
+ 𝟒𝟎𝒙 = 𝟔𝟐𝟒. Use the equation to find the length
and width of Municipal Hall.”

42. What Must be My length and Width?
The quadratic equation given describes the estimated
area of Municipal Hall of Tanay is 𝒙𝟐 + 𝟒𝟎𝒙 = 𝟔𝟐𝟒.
Find the length and width
of Municipal Hall by solving
the quadratic equation using
quadratic formula.

43. What Must be My length and Width?
The quadratic equation given describes the estimated
area of Municipal Hall of Tanay is 𝒙𝟐
+ 𝟒𝟎𝒙 = 𝟔𝟐𝟒.
Find the length and width
of Municipal Hall by solving
the quadratic equation using
quadratic formula.
𝒙𝟐 + 𝟒𝟎𝒙 = 𝟔𝟐𝟒
𝟏 𝟒𝟎 −𝟔𝟐𝟒
𝒙 =
−𝟒𝟎 ± 𝟏𝟔𝟎𝟎+𝟐𝟒𝟗𝟔
𝟐
𝒙 =
−𝟒𝟎 ± 𝟒𝟎𝟗𝟔
𝟐
𝒙 =
−𝟒𝟎 ±𝟔𝟒
𝟐
𝒙 =
−𝟒𝟎+𝟔𝟒
𝟐
𝒙 =
𝟐𝟒
𝟐
𝒙 = 𝟏𝟐 𝒙 =
−𝟒𝟎−𝟔𝟒
𝟐
𝒙 =
−𝟏𝟎𝟒
𝟒
𝒙 = −𝟓𝟐
𝒙 =
−𝟒𝟎 ± 𝟒𝟎𝟐−𝟒(𝟏)(−𝟔𝟐𝟒)
𝟐(𝟏)
𝒙𝟐 + 𝟒𝟎𝒙 = 𝟔𝟐𝟒
𝟏𝟐𝟐 + 𝟒𝟎(𝟏𝟐) = 𝟔𝟐𝟒
𝟏𝟒𝟒 + 𝟒𝟖𝟎 = 𝟔𝟐𝟒
𝟔𝟐𝟒 = 𝟔𝟐𝟒
(−𝟓𝟐)𝟐+𝟒𝟎(−𝟓𝟐) = 𝟔𝟐𝟒
2704+𝟐𝟎𝟖𝟎 = 𝟔𝟐𝟒
𝟔𝟐𝟒 = 𝟔𝟐𝟒

44. 𝒙 = 𝟏𝟐 𝒙 = −𝟓𝟐
Length is the
distance from one
end of an object to
the other. It is the
longest dimension.
Width is the
distance from one
side of an object to
the other. It is the
shortest
dimension.
What Must be My length and Width?
The quadratic equation given describes the estimated
area of Municipal Hall of Tanay is 𝒙𝟐
+ 𝟒𝟎𝒙 = 𝟔𝟐𝟒.

45. Wooh, you
found me the
solutions.
Let’s go
and find
ISabella!
You may
now
pass…

47. Is the Formula Effective?
Directions: Find the solutions of each of the following quadratic equations using
the quadratic formula. Then, decode the message.
X = 2
X = -7
X = -1
X = -9 X =
𝟏
𝟐
X = 7
X = 5
X = 0
X =
𝟒
𝟑
Finally, let us
clear this way
to see
Isabella!

48. Is the Formula Effective?
Directions: Read the situation carefully, and then solve the given
quadratic equation using quadratic formula.
“In celebration of the 417th Founding Anniversary of Tanay, Rizal, the
municipality of Tanay will host its 13th Tanay Hane Festival. Our
school is set to participate in this event as one of the contestants in
the street dancing competition. As part of our preparations for this
event, we need to create a frame for the backdrop of the dancers with
an area represented by the equation 𝒙𝟐
− 𝟏𝟐𝒙 = −𝟑𝟓.
Let's help the dancers in determining the length and width of the
frame."

49. 1. What is the correct formula of quadratic equation?
a. 𝒙 =
𝒃± 𝒃𝟐−𝟒𝒂𝒄
𝟐𝒂
c. 𝒙 =
𝒃± 𝒃𝟐−𝟒𝒂𝒄
𝟐
b. 𝒙 =
−𝒃± 𝒃𝟐−𝟒𝒂𝒄
𝟐
d. 𝒙 =
−𝒃± 𝒃𝟐−𝟒𝒂𝒄
𝟐𝒂
2. Which of the following are arranged chronologically on how to solve
quadratic equation using quadratic formula?
i. Determine the values of a, b and c.
ii. Simplify the result.
iii. Transform the quadratic equation into standard form, if necessary.
iv. Check the solutions obtained by substituting each in the original equation.
v. Substitute the value of a, b and c in the 𝒙 =
−𝒃± 𝒃𝟐−𝟒𝒂𝒄
𝟐𝒂
a. iii, i, v, ii, iv c. i, iii, v, ii, iv
b. iii, i, ii, v, iv d. i, iii, ii, v, iv

50. 3. In the given equation for the area of the frame, 𝒙𝟐
− 𝟏𝟐𝒙 = −𝟑𝟓,
which of the following represents the correct values for a, b, and c?
a. a = 1, b = 12, and c = -35 c. a = 1, b = 12, and c = 35
b. a = 1, b =-12, and c = -35 d. a = 1, b = -12, and c = 35
4. Which of the following is the correct substitution of the values a, b,
and c into the quadratic formula?
a. 𝒙 =
−𝟏𝟐 𝟏𝟐𝟐−𝟒(𝟏)(−𝟑𝟓)
𝟐(𝟏)
c. 𝒙 =
−(−𝟏𝟐) (−𝟏𝟐)𝟐−𝟒(𝟏)(𝟑𝟓)
𝟐(𝟏)
b. 𝒙 =
−𝟏𝟐 (−𝟏𝟐)𝟐−𝟒(𝟏)(𝟑𝟓)
𝟐(𝟏)
d. 𝒙 =
−(−𝟏𝟐) (−𝟏𝟐)𝟐−𝟒(𝟏)(−𝟑𝟓)
𝟐(𝟏)

51. 5. Solve the length and width of the frame with an area
represented by the equation 𝒙𝟐
− 𝟏𝟐𝒙 = −𝟑𝟓.
a. length = 5 and width = 2
b. length = 7 and width = 2
c. length = 7 and width = 5
d. length = 5 and width = 4

52. Until our next
adventure…
Here’s a
treat for
you…

53. (https://padlet.com/jodalynflores/mathema
tics-9-first-quarter-y6nqh1818ggmg39a)
What are some real-world
applications of quadratic
equations? Please post a
picture along with a short
description on our Padlet. You
can find the link and QR code
below.

55. “Commit your works to the LORD,
And your plans will SUCCEED.”
Proverbs 16:3

57. STEP 1
STEP 2
STEP 3
GROUP 1 GROUP 2 GROUP 3 GROUP 4 GROUP 5

58. 𝒙 =
−𝒃 ± 𝒃𝟐−𝟒𝒂𝒄
𝟐𝒂
a b c
STANDARD FORM
QUADRATIC FORMULA
SIMPLIFY CHECKING

59. SIMPLIFY
STEP
4 CHECKING
STEP
5

63. x² − 5x − 14 = 0
2m² + 2m = 12
2(-2)² + 9(-2) = -10
8 – 18 = -10
-10 = - 10
r² - 10r = -17
a= 2 b=9 c=10
2x² + 9x = -10
2(-
𝟓
𝟐
)² + 9(-
𝟓
𝟐
) = -10
𝟐𝟓
𝟐
–
𝟒𝟓
𝟐
= -10
-10 = - 10

65. 2x² + 9x = -10

66. Transform the quadratic
equation into standard form,
if necessary.
Determine the values of
a, b and c.

67. Simplify the result.
Substitute the value of a, b and c
in the equation 𝒙 =
−𝒃 ± 𝒃𝟐−𝟒𝒂𝒄
𝟐𝒂

68. Check the solutions obtained
by substituting each in the
original equation.