d Read the domain from the x-axis and the range from the y-axis.
A
a A parabola, see solution.
B
b h(t)=- 16t^2+280
C
c 4.18 sec
D
dDomain: 0
Range: 0
Explanation: See solution.
Practice makes perfect
a 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 decreasing curve, so it is more reasonable to use a parabola to model the data.
b Since we have recognized a parabolic shape, 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.
h(t)= at^2+ bt+c
⇓
h(t)= 16t^2+280
c We can use the calculator to estimate the time needed for the sponge to hit the ground.
Push 2nd and TRACE, choose zero from the menu and set the left bound above the y-axis and the right bound below the y-axis.
Therefore, the sponge will hit the ground after about 4.18 seconds.
d The domain is a set of t-values for which the function is defined. In this situation it is 0range is a set of all h-values a function gives. In this case 0
