Formulate:
This report will propose a total of 3 different types of equations (linear, quadratic, and cubic) which
outlines the possible performance of 3 meerkats. The meerkats: Linny, Quaddy and Cubey are running a
240-metre race where the details of the race and the results will be documented and provided to a
commentator. Therefore, graphs will be constructed and solving equations is required to determine the
functions.
Observations: Assumptions:
3 meerkats will be running a 240m race The meerkats will finish the race 5
Linny: y=mx+c seconds from each other. Eg. If Linny
Since Linny runs at a constant speed, its finishes at 20 seconds, Quaddy will finish
performance will be represented by a at 15sec or 25 sec and then Cubey will
linear equation. finish at 30 sec or 10sec. (there will be a
Quaddy: ten second gap between two meerkats)
Quaddy path looks like a quadratic This would be considered as a
function meaning there are three types professional race as this report will list all
of quadratic equations to represent the detail and abnormal occurrences of
Quaddy. The equation chosen is the race therefore, the time gap would
y=a ( x−m )( x−n ) be fairly close together.
Cubey: All the meerkats will be starting at 0
There are 4 types of cubic equations that seconds and will end at 240 metres. This
will display Cubey’s path as its path is like means the functions must be clearly
a cubic function. Cubey’s function will be identifiable. Quaddy’s function needs to
the turning point y=a ¿. have a positive a value so that it concaves
During the race, there must be at least up. If it concaves down only half of the
one point of intersection between two path can be seen which doesn’t make it
competitors. clearly identifiable as it stops at 240
The meerkats will not always be running metres. This also means that Quaddy will
towards the finish line as some may run have to run backwards until it reaches its
backwards at some points of the race. turning point, then it runs forwards. Also,
Only two meerkats are allowed to start at means that all the functions will be read
the same distance while the third one within a positive time (on the positive x-
must start either behind or in front of axis since time cannot be negative) and
them. on the whole y axis (as they are allowed
to start behind or in front of the starting
line which is 0. Or they will run
backwards where they might reach
behind the starting line)
Maths required: Technology used:
−b ± √ b −4 ( a ) ( c )
2 Desmos to accurately graph the race and
x= to verify working out
2a
Quadratic formula to find the x value. Word document to present the report
Solving simultaneous equations for point Scientific calculator to manually calculate
of intersection (substitution) the missing variables of the equation and
Use of linear, quadratic, and cubic verify the equations are correct
, functions
Solve:
Working out: Reasoning:
The predicted points are all referred to
appendix 6, the original sketch of where the
points have been established.
Linny: (30, 240) was the predicted ending point for
y=mx+c Linny therefore this coordinate was
240=m(30)+ 0 substituted into the linear equation to
determine the value m which was 8. The c
240=30 m value is 0 as the y-intercept is 0.
30
8=m
∴ y=8 x+ 0
Quaddy: The path for Quaddy was chosen to be
y=a ( x−m )( x−n ) determined by using the x-intercept form
240=a ( 35−5 )( 35−25 ) where the x-int are (5, 0) and (25, 0). Along
with the ending point of (35, 240) it was
240=a(30)(10) substituted into the function and resulted that
300 a=0.8.
0.8=a
∴ y=0.8 ( x−5 ) ( x−25 )
Cubey: The equation for Cubey was the turning point
y=a ¿ form where the turning point would occur at
40=a ¿ (20, 140). The other coordinate was the y-
intercept which was (0, 40). Hence the value a
−100=−8000 a was calculated to be 0.0125.
−8000
0.0125=a
∴ y=0.0125 ¿
Explanation: Calculations:
Each meerkat will start at 0 seconds (x value) and Since they start at 0secs and end at 240
end at 240 metres (y value). All the ending and metres these values are substituted into the
starting point calculations will be supported by equations to find the corresponding value.
desmos to strengthen reliability.
This report will propose a total of 3 different types of equations (linear, quadratic, and cubic) which
outlines the possible performance of 3 meerkats. The meerkats: Linny, Quaddy and Cubey are running a
240-metre race where the details of the race and the results will be documented and provided to a
commentator. Therefore, graphs will be constructed and solving equations is required to determine the
functions.
Observations: Assumptions:
3 meerkats will be running a 240m race The meerkats will finish the race 5
Linny: y=mx+c seconds from each other. Eg. If Linny
Since Linny runs at a constant speed, its finishes at 20 seconds, Quaddy will finish
performance will be represented by a at 15sec or 25 sec and then Cubey will
linear equation. finish at 30 sec or 10sec. (there will be a
Quaddy: ten second gap between two meerkats)
Quaddy path looks like a quadratic This would be considered as a
function meaning there are three types professional race as this report will list all
of quadratic equations to represent the detail and abnormal occurrences of
Quaddy. The equation chosen is the race therefore, the time gap would
y=a ( x−m )( x−n ) be fairly close together.
Cubey: All the meerkats will be starting at 0
There are 4 types of cubic equations that seconds and will end at 240 metres. This
will display Cubey’s path as its path is like means the functions must be clearly
a cubic function. Cubey’s function will be identifiable. Quaddy’s function needs to
the turning point y=a ¿. have a positive a value so that it concaves
During the race, there must be at least up. If it concaves down only half of the
one point of intersection between two path can be seen which doesn’t make it
competitors. clearly identifiable as it stops at 240
The meerkats will not always be running metres. This also means that Quaddy will
towards the finish line as some may run have to run backwards until it reaches its
backwards at some points of the race. turning point, then it runs forwards. Also,
Only two meerkats are allowed to start at means that all the functions will be read
the same distance while the third one within a positive time (on the positive x-
must start either behind or in front of axis since time cannot be negative) and
them. on the whole y axis (as they are allowed
to start behind or in front of the starting
line which is 0. Or they will run
backwards where they might reach
behind the starting line)
Maths required: Technology used:
−b ± √ b −4 ( a ) ( c )
2 Desmos to accurately graph the race and
x= to verify working out
2a
Quadratic formula to find the x value. Word document to present the report
Solving simultaneous equations for point Scientific calculator to manually calculate
of intersection (substitution) the missing variables of the equation and
Use of linear, quadratic, and cubic verify the equations are correct
, functions
Solve:
Working out: Reasoning:
The predicted points are all referred to
appendix 6, the original sketch of where the
points have been established.
Linny: (30, 240) was the predicted ending point for
y=mx+c Linny therefore this coordinate was
240=m(30)+ 0 substituted into the linear equation to
determine the value m which was 8. The c
240=30 m value is 0 as the y-intercept is 0.
30
8=m
∴ y=8 x+ 0
Quaddy: The path for Quaddy was chosen to be
y=a ( x−m )( x−n ) determined by using the x-intercept form
240=a ( 35−5 )( 35−25 ) where the x-int are (5, 0) and (25, 0). Along
with the ending point of (35, 240) it was
240=a(30)(10) substituted into the function and resulted that
300 a=0.8.
0.8=a
∴ y=0.8 ( x−5 ) ( x−25 )
Cubey: The equation for Cubey was the turning point
y=a ¿ form where the turning point would occur at
40=a ¿ (20, 140). The other coordinate was the y-
intercept which was (0, 40). Hence the value a
−100=−8000 a was calculated to be 0.0125.
−8000
0.0125=a
∴ y=0.0125 ¿
Explanation: Calculations:
Each meerkat will start at 0 seconds (x value) and Since they start at 0secs and end at 240
end at 240 metres (y value). All the ending and metres these values are substituted into the
starting point calculations will be supported by equations to find the corresponding value.
desmos to strengthen reliability.
