Enter the quadratic/cubic model.

Question

The table shows the temperature y (in degrees Fahrenheit) at time x, where x=1 corresponds to 1:00 AM. Use the regression feature on a graphing calculator to find a quadratic model and a cubic model for the data.

table(below)

x: 6 8 10 12 14 16 18 20

y: 2 5 8 12 13 14 12 10

Enter the quadratic model.

yq=

Enter the cubic model.

yc=

Use each rounded model to estimate the temperature at midnight.

quadratic:

cubic:

Answer 1

Putting the values in for x & y in the "list" part of "STAT" in my calculator, and using "QuadReg", followed by "Calculate", I get, rounded to the nearest thousandth, y= -0.114x² +4.137x - 18.833. If x=1 at 1 AM, x=23 at the next midnight. Graphing the function on my calculator, I get that y=5.467, or staying with whole numbers like your chart, y=5.

For a cubic model, I get y= -.008x³+.162x²+.576x -5.833. At midnight, or x=23, I get the point (23, .695). Rounding to a whole number with the cubic model, the temperature at midnight is 1 degree.

I hope this helps! Let me know if you have more questions...

Liz Z.