quadratic equation help please.

[mollykins]

I think the answer for this is a quadratic ewquation, as the graph has a curvy line but its been a yer since i've done them and i don't know how i would work this one out.

In geography, i worked out house quality and distance now i want to work out a quadratic equation ( i think it would be) to link the two. these are the sets of data i have, for the same graph and equation:

distance (miles) Quality of housing
0.7 10.51
1.6 27.32
2.1 31.42

But for the quality you could round it to 11, 27 and 31, but the distance is so small that you couldn't unles you used a different unit, which you are welcome to do aslong as you tell me which units you use and what the distance comes out as.

sorry if its realy difficult but i can't remember how to do them and even if i could its probabaly a level stuff.

[mollykins]

sorry about the numbers i'll do those again to make them clear.

distance (miles) Quality of housing
0.7.......................................10.
51

1.6.......................................27.
32

2.1.......................................31.
42

[mollykins]

the 2nd numbers in part are the decimal points after the 10 27 and 31 . . . this website isn't very good for formating stuff that was in a table.

[factor-fiction]

Im not sure you need to round- rounding from 10.51 to 11 is a 5% change.
As for distances, there's no harm in leaving as miles but if you want bigger numbers you could convert to kilometres (8 km=5 miles) or metres.
I'll come back to you on the quadratic, although I suggest that 3 readings is perhaps not enough to gib=ve reliable result

[factor-fiction]

Assuming it's a quadratic the line of best fit is
y=-7.5x² +36x-11
where x is distance in miles and y is Quality of Housing

Of course it could also be a logarithmic, exponential or other funtion, or maybe there is insufficient data to draw any conclusions

[mollykins]

We were only able to get data for three locations. Thanks thats a massive help.

[scotman]

MollyK

3 points is too few to determine any sort of function relating your data. Anything from straight line to logarithmic could be said to 'fit'