• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

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

Extracts from this document...

Introduction

Investigating the Gradients of the Graph of the Form 'y=x2' Aim To find a formula for the gradient of the graph 'y=x2'. To do this I will draw the graph and measure the gradient at certain whole numbers of 'x'. ...read more.

Middle

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 x y Gradient -3 -1 1 2 5 9 1 1 4 25 From these results I believe it is possible to deduce that the gradient of the curve at any point is equal to '2x'. ...read more.

Conclusion

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 x y Gradient 1.5 2.25 Conclusions II I can now conclude that the gradient function for a graph of the form 'y=x2' is 2x. G.F. = 2x ...read more.

The above preview is unformatted text

This student written piece of work is one of many that can be found in our GCSE Gradient Function section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Gradient Function essays

  1. Curves and Gradients Investigation

    is applied to the X value: x + h. Once this gradient has been calculated, it will give the hypothetical gradient at the point (x + h)². This gradient (i.e. 7 + h) can be converted to the gradient at the actual point in question by reducing the 'h' value to 0 so the remaining equation is the gradient at this point.

  2. Analysing Triangle Vertices and Bisectors

    Substituting x = 0 into x� + y� - 14x - 2 = 0 gives y� - 2 = 0 which, when factorised, gives y(y - 2) = 0 resulting in y = 0 or y = 2 Since point O has the y co-ordinate of 0, y = 2

  1. The Gradient Function

    Just to check that this is correct, I am now going to work out the gradient, when the tangent is at x=1. 12 = 1 1 x 3 = 3 3 x 2 = 6 If you compare the two graphs of y=x3 and y=2x3, then you can see a pattern with the curve.

  2. I have been given the equation y = axn to investigate the gradient function ...

    is know as differentiating from first principles.It is the fundamental way in which the gradient of each new type of function is found,although many shortcuts can be developed,it is important to understand this basic method FOR 2X�: Gradient = 2(x+?x)�-2x� x+?x-x = 2 [x�+3x�(?x)+3x(?x)�+(?x)�]-2x� ?x =2x�+6x�(?x)+6x(?x)�+2(?x)�-2x� ?x =?x[6x�+6x(?x)+2(?x)�] ?x Limit

  1. I am going to investigate the gradients of different curves and try to work ...

    = 5 = 10 1.5 - 1 0.5 Table of results can be seen below. I predict that for the next value, the answer will be 7. Test Chord start point 1 1 1 1 1 1 Chord finish point 5 4 3 2 1.5 6 Gradient of chord 24

  2. The Gradient Function Investigation

    h = 4(x� + 3x�h + 3xh� + h�) - 4x� (expand and simplify) h = (4x� + 12x�h + 12xh� + 4h�) - 4x� (expand and h simplify) = 12x�h + 12xh� + 4h� (cancel 4x�) h = 12x� + 12xh + 4h� (cancel h) as h tends to 0 GF tends to 12x� Both these examples have

  1. Gradient Function

    28.84 -3.1 -29.791 2.791 0.1 27.91 -3.01 -27.2709 0.270901 0.01 27.0901 -3.001 -27.027 0.027009001 0.001 27.009 -3 -27 -2.999 -26.973 -0.026991 -0.001 26.991 -2.99 -26.7309 -0.269101 -0.01 26.9101 -2.9 -24.389 -2.611 -0.1 26.11 -2.8 -21.952 -5.048 -0.2 25.24 -2.7 -19.683 -7.317 -0.3 24.39 -2.6 -17.576 -9.424 -0.4 23.56 -2.5 -15.625

  2. The Gradient Function

    Graph: Y= 4x1 The table below shows the points, which I have used to plot the graph: X Y 0 0 1 4 2 8 -1 -4 The gradient of the line is: Y2-Y1 X2-X1 = 4-(-4) = 4 1-(-1)

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work