Can someone pls help, I know this is kinda a lot but I’ve been stuck on this for a while now.

Question

The data in the table can be modeled by a quadratic function. Find the function that would fit the data.

The number of hours Temperature

after midnight

6 58

8 68

10 76

12 82

14 84

16 81

18 75

After completing the regression using this information the value of a is (__), the value of b is (__), and the value of c is (__). The equation for the situation is f(x)= (__). Use the equation to predict the temperature one hour after midnight.

Answer 1

This is a good question. So it appears as though your teacher was wanting you to utilize some plotting software such as Excel. To help you in the future for any other assignments you may get regarding making a graph and fitting the data I have provided the steps below so you are able to do this on your own in the future.

1. In Excel make two columns and label, "The number of hours after midnight", and "temperature" and put the respective numbers underneath.
2. Then draw your cursor and highlight all the numbers you want to plot, all of the numbers under each of the headings above
3. Then go to the top of Excel in click into the tab called "insert" then in the section marked "recommended charts" click the scatter plot.
4. Once your scatter plot of your data has been created you right click on one of the data points in the graph and click "add trendline"
5. A box should appear with information about your trend line, then you want to pick the option "Polynomial" under the "Trendline Options" heading and then scroll to the bottom and click the check box that says "display equation on chart".

There seems to be an issue with me adding a photo but your trend line should be f(x)= -0.4256*x^2 + 11.732*x +2.1667

Once you have done all of these steps you will get a graph like what is shown below! From here you should be able to identify the "a", "b", and "c" values according to this equation. y=f(x)=ax^2+bx+c where each of the letters "a,b,c" represent a different number in the trend line.

Once you have gotten this down as needed, to predict the temperature at 1 hour after midnight you will put a "1" in for "x" in your equation and solve for the temperature as shown below:

f(1) = -0.4256*(1) + 11.732 *(1) +2.1667 = 13.473

So this means after midnight the temperature would be 13.473 degrees (farenheit I assume). Hopefully this seems odd to you, and thats because there's very few scenarios where the temperature would dip that much in one evening, the reason this value seems so weird is because it is an approximation and when you model data it makes it very very hard to predict values that are far away from the data points you used to make your model.

Hope this helps, if not feel free to reach out!