The path of a home run ball
can be modeled by a second-degree expression.
The steepness of the centerfield seats is linear due to the steady rise.
Finding the row where the ball lands is a matter of solving a nonlinear system of equations.
There are as many nonlinear systems as there are nonlinear equations. This tool will help you understand five distinct nonlinear systems in two unknowns:
a line and a parabola,
two parabolas,
two circles,
a line and a cubic,
and a parabola and a cubic.
Choose the type of system you want to study
and fill in values for the coefficients by typing values directly into the fields or by using the sliders below the fields.
The equations are graphed, and their positions can be adjusted by dragging them in the graphing area with the mouse
or by adjusting the values in the fields manually by using the slider or by typing in the input fields.
The number of solutions will be displayed
as will the solutions themselves.
When you want to investigate another type of system, click on the appropriate button. The values you leave behind will still be there if you want to come back.
There is a practice question for you corresponding to each of the different systems,
and there are also some ideas for exploration.
Have fun comparing the different systems and seeing what you can find out about nonlinear systems.