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In this assignment I have been given the task of; 'Investigate gradients of curves'

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In this assignment I have been given the task of; ‘Investigate gradients of curves’

To accomplish this I hope to use graphs of different curves to acquire my data, which I will then tabulate and use to hopefully find a common rule for this assignment.

There are three main types of line graphs and they are divided by order. Order 1 lines are called linear and have the equation

‘y = ax + b’. Order 2 lines are called quadratic and have the equation ‘y = ax  + bx + c’. Order 3 lines are called cubic and have the equation ‘y = ax  + bx  + cx + d’. I will be concentrating on order 2 line graphs.


I predict that the rule will have something to do with the numbers before and after x in the curves’ equation.


...read more.


y = 4x     8.3      14.3       22        30        55

y = 5x      10      18.8     24.4       38        64

I then compared my results with other peoples’ results and made this table.

Curve     x = 1    x = 2    x = 3    x = 4    x = 5

y = x         2          4           6           8         10

y = 2x       4          8          12         16        20

y = 3x       6         12         18         24        30

y = 4x       8         16         24         32        40

y = 5x      10        20         30         40        50

I will be using this table to find out the rule

Analysis of my results

The number after x  multiplied by the number in front of x gives you the gradient for that curve at point x = 1. If we call the number after x ‘r’, the gradient ‘Gr’, and the number before x is ‘a’ therefore

...read more.


I think I’ve found the rule!!

rax = Gr

Let’s test it with y = 4x .

y = 4x .     r = 2   a = 4   x = 2

2 x 4 = 8   8 x 2 = 16    16 = Gr at x = 2

y = 4x .     r = 2    a = 4   x = 3

2 x 4 = 8    8 x 3 = 24    24 = Gr at x = 3



To work out the gradient at any point on my five graphs the equation ‘rax = Gr’ works perfectly.


I found that my results were slightly off from what they should be, but I compared my results with the results of others and corrected that error. The assignment had a very small margin for error, but a HUGE risk of it happening because the tangents might not be perfectly exact to the curve, as it relies upon the human eye to determine where the curve is and what direction the tangent should point in, and also the hand to draw the curve in the first place.

...read more.

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