GRAPHS(ii)

 

Contents:

 

Four Types of Graph:

Straight Line: y = mx + c.

Fig 1. y = 3x +3.

Positive: climb to the right.

Negative: climb to the left.

 

Quadratic: y = x. Fig 2.

Positive: smile shape.

Negative: upsidedown.

 

Fig 2a. y = x-5x -3.

 

 

 

 

Cubic: y = x. Fig 3.

Positive: climb to the right.

Negative: climb to the left.

 

 

Reciprocol Graphs: y = 1x. Fig 4.

Symmetrical around the origin.

Positive: top right, bottom left quadrants.

Negative: top left, bottom right quadrants.

 

 

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Area & Trapezium Rule: The area under a graph represents the total of what had been measured. The vertical axis may represent what is to be measured while the horizontal axis the time measured, ie. metres per second for distance, or goals scored in a season for total.

Example: Chart:
 Month:  Sept  Oct  Nov  Dec  Jan  Feb  Mar  Apr
 Goals Scored  7  11  10  8  14  11  9  10

 

Details entered on the graph below.

The area under the graph represents the total amount of goals scored for the whole season, 70.

 

 

The approximate area may be calculated using the trapezium rule.

Formula: Area = h((yo + yn) + y1 + y2 + y3 ... + yn-1).

Where: ('h' represents the space between each element on the 'x' axis...ie. 'h' = 1 as we take every reading). ('y' represents each reading...ie. each month's total).

y0 = 0, ie. start at a zero point.

yn = 0, ie. finish at a zero point.

y1 = 7, ie. Sept.

y2 = 11, ie. Oct...etc. 

(If the area required is for a smaller time scale, ie. Dec to Feb then: y0 would be (8), and yn would be (11)).

Formula from table: Area = 1((0 + 0) + 7 + 11 + 10 + 8 + 14 + 11 + 9 + 10) = 70.

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