• 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. The Gradient Function

    When it is only x in the curve, then the line will run through (1,1). When there is a 2x in the curve, the line will run through (1, 2). I am therefore going to make a prediction. When I demonstrate the curve of y=3x3, I am going to predict that the curve will run through (1, 3).

  1. Investigate gradients of functions by considering tangents and also by considering chords of the ...

    Therefore in the above diagram, AB and AC are chords. The gradient at A is closer to the gradient of AC than AB, since the chord AC is shorter. Every time one makes the chord shorter, the gradient of the chord gets closer and closer to the gradient of the curve at A.

  2. The Gradient Function Investigation

    gradient function of the curve: y = 2x� + 3x�, I can provide the following overview. I can see from these results that for both separate parts of the equation the X co-efficient of the gradient function (e.g. 9x�) is the same as the X co-efficient of the graph equation (e.g.

  1. The Gradient Function

    = 1,1 (X2, Y2) = 1.001, (1/X2) (X2, Y2) = (1. 001, 0.999001) Gradient = Y2-Y1/X2-X1 = 0.999001-1/1.001-1 = -0.999001 The table below shows the increment method performed, at the point (-2, -0.5)

  2. The Gradient Function

    on graph y=2x6: PREDICTIONS X=1 2 x 6 x 15 = 12 X=2 2 x 6 x 25 = 384 X=3 2 x 6 x 35 = 2916 The graph I have of y=2x6 proves that this equation is true.

  1. To investigate the effect of the constants a, b and c on the graph ...

    So by changing constant c it appears that, in this case at least, we are moving the graph up or down by the corresponding value of c. For example, on the left, we can see how graph of y = x + 5 will be moved 5 places upwards from y = x.

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

    I can say that the gradient function for the curve of y=2x� is 4x. For the curve y=3x� Tangent at x = 2 3 4 Gradient function 12 18 24 I can see that the gradient function is 6 multiplied by the point at which we draw the tangent.

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