Investigating the Gradients of the Graph of the Form ‘y=x2’

Calculations

To find the gradient on a certain point of the ‘y=x2’ graph you draw a tangent from a point. Then you form a right-angled triangle on the tangent and find the gradient as for the ‘y=ax’ graph. (As shown on graph)

e.g.

         9

                                                                         

                                                                             9-4= 5

                                                                         

                                                                        4

                                   2            3-2= 1         3 

                          gradient=y/x

                                        =5/1

                          Gradient=5

Results

From these results I believe it is possible to deduce that the gradient of the curve at any point is equal to ‘2x’.

Conclusions

I belief that that the gradient function for a ‘y=x2’ graph is 2x. To test this theory I will try it with 1.5 as the value of ‘x’.

Results II

Conclusions II

I can now conclude that the gradient function for a graph of the form ‘y=x2’ is 2x.

G.F. = 2x