Name
Semester 2
Major Assessment Task: Basketball Parabola Investigation
Subject
Challenge Maths
Year Level
9
Due Date
Conditions
Students will get 2 hours of class time and will be given at least a week after this to finish this task at
home.
Curriculum links
Year 9
Patterns and algebra
 Apply the distributive law to the expansion of algebraic expressions, including binomials,
and collect like terms where appropriate (VCMNA306)
Linear and non-linear relationships
 Graph simple non-linear relations with and without the use of digital technologies and solve
simple related equations (VCMNA311)
Year 10
Linear and non-linear relationships
 Explore the connection between algebraic and graphical representations of relations such as
simple quadratic, reciprocal, circle and exponential, using digital technology as appropriate
(VCMNA339)
 Solve simple quadratic equations using a range of strategies (VCMNA341)
 Solve equations using systematic guess-check-and-refine with digital technology
(VCMNA342)
Year 10A
Patterns and algebra
 Investigate the concept of a polynomial and apply the factor and remainder theorems to
solve problems (VCMNA357)
Linear and non-linear relationships
 Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and
their transformations (VCMNA359)
 Apply understanding of polynomials to sketch a range of curves and describe the features of
these curves from their equation (VCMNA361)
 Use function notation to describe the relationship between dependent and independent
variables in modelling contexts (VCMNA363)
Purpose



Students will increase their confidence in mathematical modelling real life scenarios.
Students will become more familiar with the key features of parabolas, specifically: turning points,
axis of symmetry
Students will develop their mathematics communication skills.
Marking Rubric
Extended
Abstract
Compares and
contrasts actual
path of ball from
parabola path
(dotted and solid
line)
Explains which
key features of
parabolas in plan
should stay
constant and
which will
change
Describes
decisions behind
method
Excludes
inappropriate
data with
reasons
Relational
Includes
coordinates/equa
tions of key
features of
parabolas
Multistructural
Identifies key
features of
parabolas
Plans method
that emphasises
independent and
dependant
variables
Calculates
average of x and
y coordinate of
vertex
Unistructural
Sketches
approximate
shape of
parabolas
Writes out a
method
Prestructural
Indicative
behaviors
Insufficient
evidence
Drawing
parabolas
Insufficient
evidence
Planning
Collects 3 vertex
data points for
each
independent
variable
increment
Insufficient
evidence
Data collection
Capabilities
Assessment
Task
Subject
Marks: _______ / 20
Comment:
Uses appropriate
data collected,
with justification
Explains how
the constants in
turning point
form of a
parabola effect
the shape of a
parabola
Demonstrates
understanding of
the meaning of
the solutions that
make a quadratic
=0
Finds turning
point equation
for all 5
independent
variable
increments
States turning
point of
parabolas
Synthesises
results and
method to
discuss factors
that affect results
Explains
recommendation
to basketball
team using
evidence
Uses evidence to
make a
conclusion
Identifies factors
that affect the
shape of
parabolas
Insufficient
Insufficient
evidence
evidence
Understanding
Use of
of quadratic
mathematical
features
reasoning
Communication
Problem solving
Basketball parabola investigation
Year 9 Challenge Mathematics
calculated from the above rubric, one mark per criteria
Basketball Parabola Investigation
Introduction:
In our Parabolas unit we are looking at how gravity affects the path of a moving object. Your
task is to design an experiment to investigate ONE of these factors (release distance from
hoop, release angle, release force, release height) and how it affects the vertical and
horizontal distance from the shooter’s hands to the vertex of the parabola. This is to help
coach the basketball team on how to more consistently get their shots in.
Aim: to investigate how (circle one independent variable: release distance from hoop,
release angle, release force, release height) affects the coordinates of the vertex of a
basketball shot (when aiming to get it in), and therefore how this independent variable affects
the turning point equation of the quadratic.
Getting knowledge ready: what do we already know about parabolas? Roughly sketch some
parabolas below and indicate their key features.
Hypothesis: as (independent variable) increases, the coordinates of the vertex of the parabola
that the basketball traces out will (describe changes in x and y coordinate of vertex)…
Draw some sketches of parabolas (at least 3) to represent how you predict the independent
variable will affect the shape of the parabola path.
Method:
Work in groups of 4 (one shooter, one cameraperson, one ball gatherer, one ruler holder)






Choose your independent variable, and what 5 increments of it you will use (which
distances, which heights, which angles, etc)
Try to make sure that all other variables are kept constant for a fair experiment (only
change the independent/experimental variable). Decide what these variables will be
and how you will ensure they stay constant.
Mark out where you will be shooting from with masking tape
Mark out where the cameraperson
Film shooting 3 shots (in) for each change in independent variable, keep the camera
steady
Watch video to obtain approximate turning point for each shot
Write out your method step by step, with your independent variable in mind:
Equipment:







1 basketball
1 meter ruler
1 video camera (phone is fine)
A makeshift tripod to hold the camera still
A basketball hoop
Masking tape
Optional: chair (careful), protractor, trundle wheel
On top of the required equipment our group will also need:
Draw a diagram of your setup, including a sketched, hypothesised parabolic path with the
key features of a parabola:
Draw a diagram of a hypothesised parabolic path overlaid onto a Cartesian plane with an
appropriate origin (recommended origin = shooters feet) and hoop coordinate.
Results (keep going until you get 3 shots in for each variable):
Indepen
dent
variable
(distanc
e,
angle,
force,
height)
Trial 1:
vertex
Coord
(x,y)
In/out/
BB?
Trial 2:
vertex
Coord
(x,y)
In/out/
BB?
Trial 3:
vertex
Coord
(x,y)
In/out/
BB?
Trial 4:
vertex
Coord
(x,y)
In/out/
BB?
Indepen
dent
variable
(distanc
e,
angle,
force,
height)
Trial 5:
vertex
Coord
(x,y)
In/out/
BB?
Trial 6:
vertex
Coord
(x,y)
In/out/
BB?
Trial 7:
vertex
Coord
(x,y)
In/out/
BB?
Trial 8:
vertex
Coord
(x,y)
In/out/
BB?
Indepen
dent
variable
(distanc
e,
angle,
force,
height)
Trial 9:
vertex
Coord
(x,y)
In/out/
BB?
Trial
10:
vertex
Coord
(x,y)
In/out/
BB?
Trial
11:
vertex
Coord
(x,y)
In/out/
BB?
Trial
12:
vertex
Coord
(x,y)
In/out/
BB?
Indepen
dent
variable
(distanc
e,
angle,
force,
height)
Trial
13:
vertex
Coord
(x,y)
In/out/
BB?
Trial
14:
vertex
Coord
(x,y)
In/out/
BB?
Trial
15:
vertex
Coord
(x,y)
In/out/
BB?
Trial
16:
vertex
Coord
(x,y)
In/out/
BB?
Did you have to omit any data collected? (think about a fair experiment) If so, leave it in the
table/s above but put a line through it or colour code it. Give reasons for omission in data
analysis. What criteria did you use to keep or “discard” data?
Analysis:
Independent
variable
Average
Average
Range
Range
vertex x
vertex y
vertex x
vertex y
coordinate coordinate coordinate coordinate
(in)
(in)
(in)
(in)
Independent
variable
Average
Average
Range
Range
vertex x
vertex y
vertex x
vertex y
coordinate coordinate coordinate coordinate
(BB)
(BB)
(BB)
(BB)
Independent
variable
Average
Average
Range
Range
vertex x
vertex y
vertex x
vertex y
coordinate coordinate coordinate coordinate
(out)
(out)
(out)
(out)
Discuss the average and range of the vertex coordinates as the independent variable changes
(what is the trend?) Were you able to keep all other variables constant or did you have to
change them to be able to get the ball into the hoop? What other factors could have affected
your results? What mistakes did you make if any, how would you change it next time? What
assumptions have been made?
Graph your 5 parabolas that have the maximum at the average vertex coordinates recorded
for your “in” shots (all on the same grid is fine).
For each of the above parabolas record the following information:
These Desmos links may be useful:
“Basketball Shot Quadratic”: https://www.desmos.com/calculator/zeqvbnno9m
“Parabola equation from 3 points”: https://www.desmos.com/calculator/elssfphm2p
Parabola Release
height (yint)
1
Vertex
(h,k)
Axis of symmetry
x=c
Equation for turning point form
y=a(x-h)2-k
2
3
4
5
Investigate (could use sliders on Desmos links above or otherwise) how each of the constants
(a, h, k) affect turning point form. Explain your findings.
Choose one of the parabolas from the table above, expand the bracket (using your knowledge
about binomial expansion, show working). Apply the quadratic formula to solve for x when
the quadratic = 0 (may need to do some research). What is the significance of the result/s?
Conclusion (summarise results, ensure you have agreed or disagreed with your hypothesis
and “answered” your aim):
What advice would you give to the basketball team to ensure they get more shots in?