Sometimes, you want to determine if a relationship exists between two variables.
One way to do this is with a scatter-plot. If you see patterns in the data, you can model the data with an equation and a graph. You will be using a graphing calculator to collect, organize, and picture the data shown below. The calculator will generate an algebraic model for the data.
1. Will this shot go in or not? Base your decision on the path of the basketball seen in the photo below.
2. Input the ordered pairs on the left-hand side into STATS mode on the calculator to find the equation of
quadratic regression for the curve.
3. Write your equation in standard form filling in values for a, b, and c. Round decimals to four places.
4. Using your equation from step 3, determine whether or not the shot will go in. You must show this step mathematically on notebook paper.
Manipulate the sliders a, h, and k to create a parabola that matches the path of the basketball to see if the shot actually goes in the hoop. Note the equation given by this curve. Does it match the equation you derived on the calculator?