We use cookies to give you the best experience possible. By continuing we’ll assume you’re on board with our cookie policy

Maths Coursework: Curve Fitting Essay Sample

  • Pages: 4
  • Word count: 1,099
  • Rewriting Possibility: 99% (excellent)
  • Category: mathematics

Get Full Essay

Get access to this section to get all help you need with your essay and educational issues.

Get Access

Introduction of TOPIC

I was firstly given the task of finding the equation of the quadratic graph which passes through the points (5,0), (3,0), (0,15). To solve this I began by drawing a rough sketch of what I thought the graph would look like with these points, as below:


(3,0) (5,0)

I worked out that the graph would look like this, and next I worked out the formula by putting the numbers I knew into brackets, and then expanding them as below. I did this because by looking at the graph you can see that when Y=0, X=5 or X=3.

Y = (x-5)(x-3) = 0

* x2-3x-5x+15

* =x2-8x+15

I worked the equation out to be Y=x2-8x+15. I then plotted this graph using omnigraph as below:

I then went onto the second task of finding the equation of the quadratic graph which passes through (0,9) and touches the x-axis at (3,0). I used the same method as before, of drawing what I thought the graph would look like:



I then put the numbers into brackets again (as below), because I worked out that when Y=0, X=3, and no other number. Then once again expanded the brackets to find the formula:

Y=(x-3)(x-3) = 0

I worked out the formula to be:


I could be sure that this was the correct equation because the co-ordinate was (0,9) which shows that the graph passes through +9, and the above equation proves this.

I decided to find the equation of the graph which passes through the points (-1,10), (2,-2), (5,4) before I worked out a method. I started by sketching what I thought the graph would look like. I also realised that the equation for all graphs is:

Y= ax2+bx+c




I the

n put the details I knew from the graph into three separate equations. I then labelled them a, b and

Sorry, but full essay samples are available only for registered users

Choose a Membership Plan










To work out these equations I had to get rid of the c’s, so I made two new equations by working out the equation c-a, and then a-b, to create equation d and e.





I then had to get either the b’s or the a’s to an equal value, so that I could work out the remaining letter. I did this by multiplying equation e by 2, so that both equations had 6b’s. This new equation was labelled f. By working out equation f and d I could work out that 18=18a as below:






I substituted a=1 into e to find:






I then substituted a=1 and b=-5 into a so that I could work out c.






So a=1, b=5 and c=4. This means that on the specified graph the equation is :



1. Firstly use the equation Y=ax2+bx+c

2. Substitute the three separate co-ordinates into three separate equations of the one used in point 1 above. For instance the co-ordinates are given in the form (x,b), x is the point that the graph crosses the x axis and b is the point where the graph crosses the y axis. So the points can be substituted so the equation is: B=ax2+bx+c

3. Number these three equations 1,2,3. You know need to get rid of the c’s, so two new equations can be made by subtracting equation 1 from 3, and labelling this equation as 4, and then subtracting equation 2 from 1, and labelling this equation as 5.

4. Now it is important to get any one letter to have an equivalent value, so use b values. Multiply equation 5 by the number of b’s there are in equation 4 and label this new equation 6. Then multiply equation 4 by the number of b’s there are in equation 5 and label this equation 7.

5. You now have to get rid of the b’s from both equations to leave you with the value of a. You do this by either adding or subtracting equation 6 and 7 together.

6. Now you have the value of -a. To find the value of a alone, divide the number value you have by -a.

7. Substitute the value for a into equation 4. From this work out b using the above rules.

8. Now substitute the values of a and b into equation 1 and then work out the value of c.

9. Now you have the values of a, b and c. Substitute these values into the equation: Y=ax2+bx+c, and this is the equation of the graph.

We can write a custom essay on

Maths Coursework: Curve Fitting Essay Sample ...
According to Your Specific Requirements.

Order an essay

You May Also Find These Documents Helpful

Numerical Methods

The place in which the graph of a line crosses the x axis is known as the root of the equation. It is not always possible to find the solution of an equation by algebraic or analytical methods such as factorising. This applies to equations such as y=3x3-11x+7. To solve equations such as these, numerical methods such as change of sign, x=g(x) and Newton-Raphson can be used to give estimates of the roots. Change of Sign Method The Change of sign method is a method used to look for when a sequence of numbers in the boundary of a root change from negative the positive or vice versa. This change means that the root of the equation is somewhere between the interval where there is a change of sign. This is the graph of the equation y=3x3-11x+7 There are 3 roots to the equation y=3x3-11x+7, this is illustrated by the...

Decimal Search

In maths equations can be solved using various methods. A very common and efficient method in solving equations is algebraically. But not all equations can be solved algebraically; these equations must be solved using numeric methods. I will study three specific numeric methods on different equations. ~ Change of sign, decimal search process. ~ Newton-Raphson method. ~ Re-arrangement method. I will be testing the numeric methods with separate equations which cannot be solved algebraically. I will also apply all of the methods to one of the equations and check if all the methods give me the same value for the root I want to find. Change of Sign, Decimal Search To find the root of the equation f(x) = 0 means finding values of x for the graph y = f(x). The change of sign method works on the bases that the y = f(x) graph changes signs when it...

Significant Study

This study aims to propose an intervention program covering the secondary mathematics subject. The academe, both faculty and students, shall benefit through having a guided program to increase the quality of the mathematics teaching-learning process. administrators and the university itself will also benefit once the proposal had been approved, executed and positively assessed, producing competent students, thus encouraging more patrons who seek for quality education. This study may also be a basis and reference for future researches and researches .The new curricula are organized in three strands of objectives: knowledge, abilities and attitudes/values. According to those we interviewed at the Ministry, one of the major aims was definitively the improvement of the attitudes of the students towards mathematics. The new curricula suggested a more intuitive approach to the mathematical concepts, with emphasis in graphical representations and real world situations. Other new features included the introduction of probability and statistics from...

Popular Essays


Emma Taylor


Hi there!
Would you like to get such a paper?
How about getting a customized one?