Use your calculator to draw a scatter plot of the data.
$10
Practice makes perfect
Let's use the calculator to draw a scatter plot of the data.
Push the STAT button, choose Edit, and enter your values.
Once the values have been entered we can plot them by pushing 2nd, Y=, and then choosing one of the plots in the list. Make sure you turn the plot ON before you choose the scatter plot type. Then, match the lists for the x- and y-values accordingly.
By pushing GRAPH the calculator will plot the data. Note that we will need to change the viewing window so that we can see all of the points.
We can see a typical parabolic shape, so let's use quadratic regression.
We can access this option by pressing the STAT button and choosing QuadReg from the CALC menu.
After matching the lists for the x- and y- values and setting the place to store the equation, move to the last line and press ENTER.
The result screen gives the coefficients of the quadratic model.
y= ax^2+ bx+c
⇓
y= -100x^2+ 2000x-1000
Since the regression equation is now stored in the memory of the calculator, when we press GRAPH again we can see the regression line with the scatter plot.
We can use the calculator to estimate the charge per ticket that maximizes the profit.
Push 2nd and TRACE, choose maximum from the menu. The calculator will prompt us to choose a left-bound, a right-bound, and to provide the calculator with a guess as to where the maximum might be. Be sure to choose the bounds appropriately so that the maximum is between these values.
Therefore, the profit-maximizing charge per ticket is $10.
