A collection of tasks from peer presentations in the eTwinning project "The Hidden World of Parabolas".

1. Peer
presentations
in eTwinning
project
"Hidden World
of parabolas"
Teams:
I,II,III,IV,VI,VIII,X
III and XVI

2. Hidden World of Parabolas
Team 1
eTwinning collaborative presentation
Debelić Vito
Dorian Fafanđel
Beg Antonija
Nadja Dončić
Tamara Jovanović
Aleksandar Jovanović
Azra Y.
Burçin B.
Damla T.
Melike A.

3. My bridge using Desmos or Geogebra
We can make your own bridge construction using parabolas!
Source: https://twitter.com/kbridgescarter/status/829503601252892672

4. A Task with Answers:
1. What is the domain for the following function: y=4(x-5)² -7
❏ (♾️,-♾️)
❏ (-♾️,♾️)
❏ [♾️+1,-♾️-1]
❏ [-♾️,5]
Author: Nađa Dončić

5. A Task with Answers:
2. For x = 4 the function f(x) = x² + bx + c achieves a minimum value equal to -9. What is c?
❏ -8
❏ -7
❏ 7
❏ 8
A
Author: Dorian Fafanđel

6. Hidden World of Parabolas
Team 2
eTwinning collaborative presentation
David Žujić
Vojkan Veselinović
Milica Mandić
David Žujić
Mihails Nečajevs
Jevgenij Angerman
Eugene Gofenshefer
Simay O.
Segah Beril Y.
Fatmanur A.
Ersel G.

7. Team presentation

8. Simone Biles was the first gymnastics that succeed
this jump and that is why it is called the Biles double
layout. This quadratic function can be used to describe
that practice.
Jelena М.
Quadratic function and gymnastics

9. VECİHİ HÜRKUŞ
Aviation contributions:
In 1917, Hürkuş became the first Turkish aviator to fly a twin-engine aircraft, a Russian Caudron G.4 captured at the
Caucasian Front. In 1918 he manufactured a propeller from scratch in Istanbul, for a Nieuport 17 also captured from
the Russians. During the Turkish War of Independence he produced adhesive from gelatin to glue fabric to aircraft
wings.
In 1923, in Edirne, Hürkuş flew an abandoned Italian Caproni Ca.5 aka Ca.57 or Breda M-1 with nine passengers, the
first Turkish pilot to fly a passenger aircraft. He constructed the country's first gliders (US–4 ve PS–2), and played a
role in the establishment of the Turkish Bird(Turkish Aviation Society) from 1935 to 1936 in Etimesgut, Ankara.
During his flying career, which spanned a period of 52 years (1916–1967), Vecihi Hürkuş flew a total of 102 different
models of aircraft and spent 30,000 hours (3.4 years) in the cockpit.

10. A helicopter which bears his name, acts as given in the figure above.
The way of the helicopter corresponds to the graph of the function
y = f(x) = – 0,0024 . x2 + 0,24 . x
a-) How many kms far the helicopter lands on? Let's find out.
b-) Let's find the maximum height reached by the helicopter.
c-) Let's find the gap that helicopter's rise continuously.
d-) Let's find the gap that helicopter's descend continuously.
QUESTION

11. ANSWER
a-) y = f(x) = – 0,0024 . x2 + 0,24 . x = 0
x . (– 0,0024. x + 0,24) = 0
=> x = 100 is found.
b-)
y = f(x) = – 0,0024 . x2 + 0,24 . x & y = f(50) = – 0,0024 . (50)2 + 0,24 . 50 => y = 6 km is
found.
c-) The gap that helicopter's rise is [0,50] as it is seen in the graphic.
d-) The gap that helicopter's descend is [50,100].
Ersel G.
Babaeski Şehit Ersan Yenici Anatolian High School

12. QUESTION
In a football game, Ali passes to his friend Cengiz as shown in the figure.
Since the function of the path followed by the ball is calculated as f(x)= -4x2+36
A) How meters can the ball rise from the ground?
A) What is the distance between Ali and Cengiz?

13. ANSWER
• A) x=0 =>f(0)= -4.(02)+36 => y=36
• B)y=0 => -4x2+36=0
-4x2=-36 =>x2=9 => x=-3 or 3
Accordingly, the distance between Ali and Cengiz is 6
meters.
Ersel G.
Babaeski Şehit Ersan Yenici Anatolian High School

14. Babaeski Sinanlı Bridge
The Sinanlı Bridge will be restored. For this, a platform
was installed under the central arch. The distance between
the highest point of the arch and the platform is 7.2 meters.
4 equal spaced supports will be placed between the
platform and the arch as shown in the figure. What is the
total length of the supports to be used for this job?
It is a stone arch bridge built by
Mimar Sinan by Sokullu
Mehmet Pasha in the second
half of the 16th century. The
bridge is 123 meters long and
the span of the central arch in
the form of a parabola is 20
meters.
QUESTION
7,2 m
20 m

15. ANSWER
Simay O. and Fatmanur A.
Babaeski Şehit Ersan Yenici Anadolu Lisesi

16. A Task with Answers:
Which of the following is correct for the vertex of the f(x) = -3x^2 + 12x + 1?
A. There is a local minimum at (-2, -35)
B. There is a local maximum at (-2, -35)
C. There is a local minimum at (2, 13)
D. There is a local maximum at (2, 13)
Milica M., The First High School of Kragujevac
Fun fact: The Name “Parabola”
The Greek mathematician Apollonius of Perga (third to second centuries B.C.) is credited
with naming the parabola. Parabola; is from the Greek word meaning “exact application,”
which, according to the Online Dictionary of Etymology, is “because it is produced by
‘application’ of a given area to a given straight line.”

17. A Task with Answers:
Author: Segah Beril Y, Babaeski Şehit Ersan Yenici Anadolu Lisesi

18. A Task with Answers:
What are the points of intersection of the line with equation 2x + 3y = 7
and the parabola with equation y = - 2 x 2+ 2 x + 5?
❏ 1 The points of intersection are : (2 , 0) and (-2/3 , 29/5).
❏ 2 The points of intersection are : (2 , 1) and (-2/3 , 29/5).
❏ 3 The points of intersection are : (2 , 3) and (-2/3 , 29/5).
❏ 4 The points of intersection are : (2 , 4) and (-2/3 , 29/5).
Author: David Ž. The First High School of Kragujevac

19. Hidden World of Parabolas
Team 3
eTwinning collaborative presentation
Uroš Ignjatović
Boran Bubanja
Aleksa Đurišić
Ivana Rajković
Aleksandra Aleksandrović
Aleksandra Aćimović

20. There is geometry in the humming of the strings, there is music in the spacing of the spheres.
Pythagoras
AĐ

21. Maths in Music
Notes has an existing relationship with one another. Below
is the illustration of the relationship among notes based on
their values.
AĐ

22. Pressing down at the 12th fret makes the string half of its
full length, which produces an “Octave” or “High 8th” note.
UI

23. If we start with the string of certain thickness, then the pitch
depends of her length: the shorter the wire is, the pitch rises. if we
shorten the wire into its half (ratio 2:1), the tone will rise by an
octave; if we shorten the wire for one third (ratio 3:2), the tone will
rise for the fourth; if we shorten the wire for one fourth (ratio 4:3),
the tone rise for the fifth.
UI

24. Math explains how tones are made, and
by what principles compositors make
wholes of them.
The way of thinking while playing is
similar to the way of thinking while doing
some mathematical proof or procedure.
BB

25. •Whole note has two halfs, four quarters, eight-eighths. One half
has 2 quartrs, four-eighths, etc. It reminds us of a friction which is
really what it is.
•For example, if we would take sixteenths instead of eighths, we
would be having more notes to play, because of what the melody
would sound faster.
BB

26. Parabola on musical instruments
Learning to play a musical instrument relies on
understanding concepts, such as fractions and ratios,
that are important for mathematical achievement.
AĐ

27. AĐ

28. AĐ

29. •Mathematically speaking, the modifications to the strings
have the effect of dividing an exponential function by some
kind of polynomial.
•We can find a polynomial that fits the exponential well, and
gives us strings of the same length.
AĐ

30. •Exponential growth is initially slow, so that (starting at the
right of the harp), growth in string length is slower than the
linear shift provided, which means that the top of the harp
curves down.
•After a few octaves, growth in string length speeds up, and
so the top of the harp curves up again.
AĐ

31. AĐ

32. Hidden World of Parabolas
Team 4
eTwinning collaborative presentation
Şahin Şen Girls
Anatolian Imam Hatip
High School
Srednja škola
Markantuna de Dominisa
Rab
Halime A
Fatmanur F
Sude Y
Ivan Lukas Andreškić
Lucija Barčić
Martina Tea Barčić
Stela Fafanđel

33. CARL FRIEDRICH GAUSS
“MATHEMATICS IS THE QUEEN OF THE SCIENCE”

34. Connection of mathematics with other school subjects
1. Each student make a page with an example.
2. Each student discover with which subject is correlated some other example.

35. An example
U fizici, parabola (točnije, krivulja) je ravna ili
zakrivljena crta na grafu koja pokazuje kako se
vrijednosti jedne veličine mijenjaju u odnosu na
promjenu vrijednosti druge veličine.
Parabolu u fizici možemo pronaći kod
vertikalnog hitca, kao što je prikazano na slici.
- Stela Fafanđel
Fizika (Physics)
A school subject (correlated with this example)

36. Fatmanur F(Şahin Şen Girls Anatolian Imam Hatip High School)

37. An example
Parabolic mirror. A concave mirror whose cross-
section is shaped like the tip of a parabola. Most of
the light, radio waves, sound, and other radiation
that enter the mirror straight on is reflected by the
surface and converges on the focus of the
parabola, where being concentrated, it can be
easily detected
Halime A(Şahin Şen Girls Anatolian Imam Hatip
High School)
(www.dictionary.com )

38. An example
After the trough obstacle reflects
the linear woves coming from the
obstacle, the woves gather at the
focal point of the obstacle. The
parabolic wove from the focus of
the hollow obstacle reflect lineary
from the obstacle
(Fatmanur F-Halime A/Şahin Sen)

39. An example
Horizontal jump movement is a movement of two
dimensions. Moves along both the x axis and the y-axis. The
combination of the two creates the horizontal jump
movement trajectory. The trajectory of the ball thrown
horizontally from the top of a high building is as in the picture
next door. I mean, it's parabolic.
(Şahin Şen Girls Anatolian Imam Hatip High School)
A school subject (correlated with this example)

40. Hidden World of Parabolas
Team 6
eTwinning collaborative presentation
Nisa A.
Berivan B.
Zahirşah B.
Kuparić Mario
Miš Andro
Paparić Ana
Paparić Lucija
Boško Stojković
Aleksandar
Obradović
Igor Memarović

41. TASK:
Each student write a task for the quiz with multiple
answers (we prefer 4).
You can add interesting things about the parabola,
some pictures, illustrations, ...
The Name "Parabola"
The Greek mathematician Apollonius
of Perga (third to second centuries
B.C.) is credited with naming the
parabola. "Parabola" is from the
Greek word meaning “exact
application,” which, according to the
Online Dictionary of Etymology, is
“because it is produced by
‘application’ of a given area to a
given straight line.”

42. A Task with Answers:
Author: Boško Stojković, II7
Which of the following is correct
for the vertex of the parabola
f(x) = 2x2 + 8x - 12 ?
A:There is a local minimum
at (-2, -20)
B:There is a local maximum
at (-2, -20)
C:There is a local minimum
at (2, 12)
Galileo and Projectile Motion
In Galileo’s time, it was known that bodies fall
straight down according to the rule of
squares: The distance traveled is proportional
to the square of the time. However, the
mathematical nature of general path of
projectile motion was not known. With the
advent of cannons, this was becoming a topic
of importance. By recognizing that horizontal
motion and vertical motion are independent,
Galileo showed that projectiles follow a
parabolic path. His theory was eventually
validated as a special case of Newton’s law of
gravitation.

43. A Task with Answers:
Author:Nisa A, Babaeski Şehit Ersan Yenici Anadolu Lisesi
2.

44. A Task with Answers:
Author:Berivan B, Babaeski Şehit Ersan Yenici Anadolu Lisesi
3.

45. A Task with Answers:
Author:Zahirşah B, Babaeski Şehit Ersan Yenici Anadolu Lisesi
4.

46. A Task with Answers:
5. Which of the following numbers is the larger solution of the equation 2x2 = 7x - 3?
A) -3
B) -0.5
C) 0.5
D) 3
f(x) = -0.3x2 + 0.2x + 3.8
In the picture you can see inside the church Colònia Güell which is located in
famous park “Park Güell” in Barcelona.
Author: Ana Paparić, Srednja škola Markantuna de Dominisa Rab

47. A Task with Answers:
When a cone is cut with a plane as in the figure, a
parabola with the equation f(x)=-0,6x2+4,1 is
obtained. So what is f(1)?
A)3 B)3,5 C)4 D)4,1
Author:Nisa A., Babaeski Şehit Ersan Yenici
Anadolu Lisesi
Apollonius’ Cone Sections
Apollonius (262-190 BC)
showed that if we slice a
cone with a plane, we
would get three different
geometric shapes
depending on the angle the
plane made with the
ground plane. These are
circle, ellipse, and
parabola.
6.

48. A Task with Answers:
7. What is the sum of the coordinates of the points where
the parabola given by the f(x)=2x2-6x+4 equation crosses
the x axis?
A)-3 B)-1 C)2 D)3
Author:Berivan B.,Babaeski Şehit Ersan Yenici Anadolu Lisesi
In architecture, parabola is
used in structures such as
mosque dome, portico,
bridge, inner carrier
column, opera house.

49. A Task with Answers:
A beam coming out of this light bulb hits the parabolic
surface and proceeds along the line x = 2. According to
this, what is the ordinate of the point where the beam hits
the parabolic surface?
A) 0,3 B) 0,6 C) 0,9 D) 1
Author:Zahirşah B.,Babaeski Şehit Ersan
Yenici Anadolu Lisesi
It consists of headlight,
parabola mirror or
reflector, headlight glass
with diffusing feature and
light source. The parabola
mirror reflects the light
into a bundle and
increases its intensity.
The headlight glass
distributes the light from
the reflector in the desired
direction. As a light
source, halogen bulbs,
two filament bulbs or
xenon headlight systems
are used.
At the focus of a parabolic surface
modeled by the equation
f(x)=0,15x2, there is a light bulb.
8.

50. Hidden World of Parabolas
Team 8 eTwinning collaborative presentation

51. Adana Seyhan
Şehit Fatih YENİAY
Anatolian High School.
Secret World of Parabolas Team VIII presentation.
Necmiye Doğruyol, Esra Gündüz, Çağla Susuz, Berfin Aslan,
Gamze Güğer, Zehra Turğut, Hatice Ceylan, Zekiye Tarhan,
Görkem Orçun Burhan, eTwinning team OŠ”Osman Nakaš”

52. ZEKİYE
TARHAN

53. GAMZE GÜGER

54. BERFİN ASLAN

55. ESRA GÜNDÜZ
ÇAĞLA SUSUZ

56. NECMİYE DOĞRUYOL

77. ADANA SEYHAN
ŞEHİT FATİH YENİAY
ANATOLIAN HIGH SCHOOL
"THE HIDDEN WORLD OF PARABOLS"
eTwinning team OŠ”Osman Nakaš”,
Sarajevo
PROJECT STUDENTS THANK YOU FOR
ACCEPTING THIS PROJECT.

78. Hidden World
of Parabolas
Team 13
eTwinning collaborative
presentation
Aleksandar Jovičić
Martina Lukić
Magdalena Pavlović

79. Did you know that parabolas are everywhere
around us?
Aleksandar Jovičić

80. Every fontain contains a lot of parabolas.
Martina Lukić

81. There are so many parabolas that we
meet in everyday life.
Magdalena Pavlović

82. Hidden World of Parabolas
Team 16
eTwinning collaborative presentation
Andreja Maksimović
Dunja Milenković
Angelina Peulić

83. a=-6
b=0
c=0

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

85. a=1
b=0
c=0

87. Thank you!