SCIE1000 Chapter Notes - Chapter 3: Quadratic Equation, Linear Model
Chapter 3 summary !
Linear models
Find the expression of error for two functions
"!
•Expression of error: a function showing the difference between the functions !
•First function - second function = function of the difference !
Linear model: meaning of each term !
!
How to find linear models given graph
!
•Find two coordinates and use the m=rise/run formula to find the gradient (find the units for m)!
•Find the y intercept by looking at graph and estimating. !
Draw a linear graph given model
"!
•Plot the y intercept !
•Plot another two coordinates very distanced from each other (include the coordinates next to
the plots in brackets)!
•Draw the straight line !
•Label x and y axis (including units)!
•Title the graph !
Limitations of the model !
•Can only be used for perfectly linear data because this model will not show any fluctuations in
data!
•Good for showing the general trend line of data!
•If the model was extracted by hand from looking at the graph, it is prone to personal calculation
errors!
•Linear equations will not show the minimum value of the data (only the initial value from when
the data was first being calculated). !
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Document Summary
Find the expression of error for two functions: expression of error: a function showing the di erence between the functions, first function - second function = function of the di erence. How to nd linear models given graph: find two coordinates and use the m=rise/run formula to nd the gradient ( nd the units for m, find the y intercept by looking at graph and estimating. How to estimate the constants of the quadratic equation from graph. Can be seen by looking at the graph. Limitations of quadratic models: if the data only shows a small window of the quadratic function, then trying to extrapolate data that go beyond what is given can be problematic. This is because at speci c x values, the function can reach a minimum or maximum and then begin to decline/incline which may not be a possible trend for the speci c scenario you are working with.
