Modeling Prompt

To introduce the task, make sure students can easily visualize what shape is made by water coming out of a jet or fountain. Ask students what shape water makes when it comes out of a drinking fountain, and either sketch the shape for all to see or invite a student to sketch it. Ask if they have seen fountains with jets that shoot water. Consider showing examples of a few, including videos if possible. Here is an example image:

An important point to highlight is that the water makes a curved path through the air that can be modeled by a quadratic function.

Then take students through a simplified version of the task, with one statue and one water jet. Here is an image to use if needed. The trapezoid represents the statue and the red dot is the location of the water jet.

Ask students what they would need to know in order to write an equation for a path for the water that would make it go over the statue (the distance from the jet to the statue, the height of the statue). Fill in reasonable heights and distances.

Then ask, “What strategy would you use to find an equation for the path of the water?” (Use the given distances to represent the statue and the location of the jet on a coordinate grid, then write a vertex form equation by choosing a reasonable vertex and adjusting parameters as needed.) After some quiet think time, ask students to share their ideas with a partner before inviting students to share with the class.

If no student suggests estimating a reasonable vertex for the water’s path and writing a vertex form equation, ask students to discuss this idea. Vertex form is a very convenient way to write the equation if we know the size and distance of the statue so we can represent it on a coordinate grid.