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

A suitable tool makes short work of this. Most spreadsheets and graphing calculators will do quadratic regression. All you have to do is enter the data and make use of the appropriate built-in functions.

Desmos will do least-squares fitting of almost any function you want to use as a model. It tells you ...

a = -0.425595

b = 11.7321

c = 2.16667

so

f(x) = -0.425595x² +11.7321x +2.16667

and f(1) ≈ 13.5

_____

Additional comment

Note that a quadratic function doesn't model the data very well if you're trying to extrapolate to times outside the original domain.