Quadratic equations/scatter plots

Question

Create a scatter plot and determine the linear or quadratic function that best models each set of data. Round coefficients to the nearest hundredth.

x Y

______

-4 / 25

-2 / 15

0 / 6

2 / 10

3 / 16

5 / 18

Answer 1

I'll assume you can make a scatterplot.

I'm going to assume you get to use your calculator to do this. It becomes quite a bit more complicated if you are required to do this manually but if you are, message me, and I'll help you.

If you have a calculator similar to a TI-84 Plus CE, you can enter the data in lists by pushing the "stat" button, and entering "1: Edit". You will be taken to a screen with lists L1, L2, etc on it. Enter the x-values in L1 and the y-values in L2

To fit a linear function to the data points. press the "stat" button again and scroll right to "CALC" in the upper menu then scroll down to "4: LinReg (ax + b). Make sure the Xlist says L1 and the Ylist says L2 then just scroll down to "Calculate" and push enter.

You should get a screen that says:

y=ax+b

a=-0.578313253

b=15.38554217

r²= 0.0856760375

r=-0.2927046933

If you are missing the last two entries, push the "catalog" button (the blue 2nd button then "0") and scroll down to "DiagnosticsOn" and hit enter twice (it should say "Done") then repeat the process and you should see the last two entries.

The r² is how good a fit the line is to the data points. You want a number close to "1" to be a good fit. In this case, it's not a good fit (the number is close to zero).

To fit a quadratic function to the data points, repaet using the "stat", "CALC", and "5:QuadReg". When you get the results, compare the r2 values. Whichever is closest to the number 1 is the best fit. It will be the quadratic.

The equations are built using the numbers given and the generic equation given. Just plug in the values for a, b, etc.