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

The Gradient Function

Extracts from this document...

Introduction

The Gradient Function

x=a’ is a vertical line which intercepts the x-axis at point ‘a’.

‘y=a’ is a horizontal line which will intercept the y-axis at point ‘a’.

‘y=ax’ and ‘y=-ax’ are the equations for a sloping line which intercepts at the origin. The value of ‘a’ is the gradient of the line, so therefore the larger the value of ‘a’ the steeper the gradient of the line.

I am trying to find the gradient function this is a formula that will work out the gradient of any line.

...read more.

Middle

x

-3

-2

-1

0

1

2

3

x2

9

4

1

0

1

4

9

y

9

4

1

0

1

4

9

(See graph, fig.1)

From the graph we can see that as the values of the coordinates increases, so does the gradient. We can see this from the

...read more.

Conclusion

‘y’ value’s by squaring the ‘x’ value. The closer the two points the more accurate the result will be, for example if we choose ‘2’ as the first ‘x’ value we could then choose ‘2.001’ as the next ‘x’ value. The gradient is found using the equation:

Gradient=y1-y2

                                                     x1-x2

So using the example numbers from above I would find the gradient as shown below:

Gradient=y1-y2

                                                     x1-x2

=4.004001-4

2.001-2

Gradient =4.001

This method is more accurate than using the results from the graph. This is because when taking results from the graph it is very difficult to get them as precise.

...read more.

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. Peer reviewed

    The Gradient Function Coursework

    5 star(s)

    The following equation denotes this: dy ?y dx ?x By finding dy / dx from y I used a procedure called differentiating y with respect to x. The gradient function I developed is indeed a generally used function in calculus, and this backs up the findings of this assignment.

  2. The Gradient Function

    I am once again going to substitute the values into the equation. . The Change in Y = 1 = 3.3 The Change in X = 0.3 As you can see, this isn't exactly the most accurate answer either. If you calculate it correctly, -0.5 x 6 = -3.

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

    will now test for the line y = -2x+5 ,and according to the formula the gradient should be equal to -2 After drawing the graph for y=-2x+5 I have arrived at the following results: Y=-2x+5 Gradient function -2 I have arrived at the conclusion that the gradient function is =

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

    The gradient of the tangent will equal the gradient of the curve at that point. (1,2) Gradient = difference in y values = 2.25 = 2.25 difference in x values 1 (2,5) Gradient = difference in y values = 4 = 4 difference in x values 1 (3,10)

  1. The Gradient Function

    is: nx(n-1) Proving the General Formula To prove the general formula, it was necessary to expand the brackets (x + d)n. This proved quite difficult and several sources of information were used including books on the subject and the Internet.

  2. The Gradient Function Investigation

    - x5 (expand and h simplify) = (x + h)(x + 4x�h + 6x�h� + 4xh� + h ) - x5 (expand h and simplify) = (x + 5x h + 10x�h� + 10x�h� + 5xh + h ) - x5 h (expand and simplify) = 5x h + 10x�h� + 10x�h� + 5xh + h (cancel x5)

  1. Gradient Function

    0.4 23.56 2.7 19.683 7.317 0.3 24.39 2.8 21.952 5.048 0.2 25.24 2.9 24.389 2.611 0.1 26.11 2.99 26.7309 0.269101 0.01 26.9101 2.999 26.97301 0.026991001 0.001 26.991 3 27 3.001 27.02701 -0.027009 -0.001 27.009 3.01 27.2709 -0.270901 -0.01 27.0901 3.1 29.791 -2.791 -0.1 27.91 3.2 32.768 -5.768 -0.2 28.84 3.3

  2. The Gradient Function.

    I am now going to look at the line y=c. I already know the gradient of the line, as you can tell from the equation the gradient is always going to be one as there are always going to be the same values as each other.

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