Finding the equation of a straight line is easy Just use y = mx + c Finding the equation of a quadratic curve from a set of data is more difficult. We have to convert it into a straight line – this is called Linearising Linearising a Quadratic Curve 1

Graph of distance against time time Distance Linearising a Quadratic Curve 1 TimeDistance

Using your knowledge of completing the square the equation is y = a(x + b) 2 + c a = vertical stretch b = horizontal translation c = vertical translation In our case b = 0 No Horizontal translation So y = ax 2 + c time Graph of distance against time Distance

To find a and c make a new table of values of x 2 where x 2 = X So y = aX + c Time xDistance yTime 2 X = x 2 Distance y

Now a straight line is obtained The gradient is m = The y intercept is c = – The equation is y = X – Replace X by x 2 y = x 2 – So distance =  time 2 – Graph of distance against time 2 y = X X distance y

Finding the equation of a quadratic curve 2 No. of days x No. of cases y Graph of No. of cold cases against no. of days days No. of cases Plot the points and workout the horizontal translation of the maximum

The horizontal translation is x = 10 as the maximum occurs at x = 10 It has also been flipped, stretched vertically and translated vertically Using your knowledge of completing the square The equation is y = a(x + b) 2 + c a = vertical stretch b = horizontal translation c = vertical translation Graph of No. of cold cases against no. of days days No. of cases

In our case b = –10 as it has been translated 10 to the right y = a(x - 10) 2 + c To find a and c make a new table of values of (x–10) 2 So y = aX + cwhere X = (x–10) 2

No. of days x No. of cases y X (x–10) 2 No. of cases y Now plot a new graph of X = (x–10) 2 and y = No. of cases Find the equation of the line of best fit Do this by hand, Excel and the calculator to provide the required checks

Graph of No. of cold cases against (x-10) 2 y = x (x-10) 2 no. cold cases Now a straight line is obtained The gradient is m = – The y intercept is c =

The equation is y = –0.8447X Replace X by (x – 10) 2 y = –0.8447(x – 10) Multiply out the brackets y = –0.8447(x – 10)(x – 10) y = –0.8447(x 2 – 20x + 100) y = –0.8447x x – y = –0.8447x x

No. of cases = –  No. of days  No. of days This is very similar to the quadratic curve of best fit in the original graph This equation can be used to work out the no. of cases if you are given the no. of days Eg If days =10 then No. cases = –   = Actual value = 105 % error =