Use your calculator to draw a scatter plot of the data.
Function: - 16+6x+22 5 feet above the ground: after 1.235 sec Time in the air: 1.375 sec
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 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= - 16x^2+ 6x+22
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 how long is the skier in the air.
Push 2nd and TRACE, choose zero from the menu and set the left bound above the x-axis and the right bound below the x-axis.
This means that the skier was in the air for 1.375 seconds. To find out when the skier was 5 feet above the water, we have to substitute 5 for y in the equation and calculate x.
Let's substitute the coefficients into the Quadratic Formula.
x=- 6±sqrt(6^2-4(-16)17)/2(- 16)
Since x is the time it cannot be negative, so the sign in front of the square root has to be positive for the fraction to be positive.
x=- 6-sqrt(6^2-4(-16)17)/2(- 16)≈ 1.235
Therefore, the water-skier is 5 feet above the ground after 1.235 sec.
