The table shows a meteorologist's predicted temperatures for an April day in Washington D.C. Use quadratic regression to find a quadratic model for this data. (Use the 24-hour clock to represent times after noon.)

Time

Predicted Temperature (oF)

8 a.m.

50.68

10 a.m.

62.24

12 p.m..

69.75

2 p.m..

73.2

4 p.m...

72.59

6 p.m..

67.93



(1 point)
Responses

–0.007x2 + 15.907x – 40.131
–0.007 x 2 + 15.907 x – 40.131

–0.507x2 + 14.907x – 36.131
–0.507 x 2 + 14.907 x – 36.131

–0.507x2 – 14.907x + 36.131
–0.507 x 2 – 14.907 x + 36.131

–1.007x2 + 13.907x – 32.131

1 answer

To find a quadratic model using quadratic regression, we need to find the equation of the form y = ax^2 + bx + c that best fits the data points.

Using the given data:

Time: [8, 10, 12, 14, 16, 18]
Predicted Temperature: [50.68, 62.24, 69.75, 73.2, 72.59, 67.93]

We can plug these points into a regression calculator or software to find the quadratic equation. After performing the regression, we find the equation:

-0.507x^2 + 14.907x - 36.131

So, the correct answer is:

–0.507x^2 + 14.907x - 36.131