Outcome C3: sketch tables and graphs from descriptions and collected data
Origionator: Alec (Quadratic Function tables and graphs). Alison and Kyle (Exponential Function tables and graphs)
When data is collected, it can be arranged into a two column table, one column for the independant variable (x), and one column for the dependant value (y).
Example:
|
x
|
y
|
|
1
|
1
|
|
2
|
4
|
|
3
|
9
|
|
4
|
16
|
|
5
|
25
|
|
6
|
36
|
From the table, one is able to plat the values of the collected data on a scatter-plot graph.
Example:
The general form for the equation of this graph is: y= ax2 + bx + c. It may also be in standard form, which is: y = a(x – h)2 + k, or intransformational form, which is: 1/a(y-k)=(x-h)2
One is then able to determine the equation of the graph by using quadratic regression, or by determining the stretch(a), vertex (h,k), y-intercept (c), and x-intercepts (or "roots") algaebraically and by using the quadratic formula. However, not all these values need to be determined to graph the function.
A common real-life situation in which something like this would occur would be when and object is thrown into the air. The shape of the path the object will travel will be a parabola. One could then gather certain heights the object reaches and compare them with the distances the object travels in a table, or certain heights object reaches and compare them with time the object is in the air in a table, or compare distances the object travels and time the object is in the air in a table.
Example:
Joe throws a tennis ball in Bill's direction. The ball reaches a maximum height of 25 metres above the ground at a horizontal distance of 30 metres, and Bill stands 50 metres away from Joe. Joe stands 1.5 metres tall, and Bill 1.8m. Will the ball be caught by Bill, or be overthrown or underthrown?
One would gather the data from the problem and arrange it in a table.
|
x
(distance)
|
y
(height)
|
|
0m
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1.5m
|
|
30m
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25m
|
The points could then be plotted on a scatter plot graph, and then connected to form the parabolic path the ball travels.
The problem could then be solved algebraically or by using quadratic regression on your calculator
Comments (1)
Anonymous said
at 8:04 pm on Mar 13, 2007
Nice work Alec... but you never finished solving your sample problem.
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