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Maths Coursework: Curve Fitting

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Introduction

Maths Coursework: Curve Fitting                        

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:

(0,15)image00.png

image03.pngimage02.png

                (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:


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Middle

image05.png

(3,0)

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:

Y=x2-6x+9

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

image06.png

(-1,10)

(5,4)

image01.png

(2,-2)

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

a

4=a(52)+b(5)+c

4=25a+5b+c

b

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Conclusion

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.Now you have the value of –a. To find the value of a alone, divide the number value you have by –a.Substitute the value for a into equation 4. From this work out b using the above rules.Now substitute the values of a and b into equation 1 and then work out the value of c.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.

Page:

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