Learning Objective: The study of parabolic curves through the design of water arcs. Students can work alone or with one partner. Due date is posted in Blackboard. Overall Project Plan: You have been hired to design the water arc of a coin fountain. You will design your fountain, show your fountain on a graph, and represent the equation in different algebraic forms. PART ONE 1. Design your fountain by selecting where the water will launch, where it will land, and the height of the water arc. Follow specifications below for your launch point, landing point, and the height of your water arc. Launch and Landing Points: You will use the x-y axis to design your fountain. The circular pool of the fountain has a diameter of 20 feet. Let the surface of the pool correspond to the x-axis with the left side of the pool at the origin (0,0). Choose your launch and landing points (aka where the water comes out of the fountain and where the water goes back into the fountain) to meet the following conditions: Your launch point and landing points must be in the water (for example you can't launch/land from the edge of the pool. In other words, your launch point must be greater than 0 and your landing point must be less than 20.) Hint: To make your algebra manageable for this project, choose integer values for your launch and landing point that create an integer for your input value of the parabola's vertex. For example, if I use a launch point of 2 feet and a landing point of 18 feet, then the input value of the vertex would be half-way between 2 ft. and 18 ft. Hence the input value of the vertex would be 10 feet (10 is an integer). But, if I choose a launch point of 2 feet and a landing point of 7 feet, then I will get an input value of my vertex of 4.5 feet (4.5 is not an integer). If your input value of your vertex is a non-integer, it will magnify the intensity of the algebra for this project. Height of Fountain: Choose the height of your fountain (aka the height of the water arc) to meet the following conditions: The height of the water arc must be greater than 6 feet, but less than 30 feet. The height of the water arc should be non-integer. An example of a height that would meet the specifications is 28.2 feet. (Students should use different height for their project, this is just an example of non-integer value that meet the conditions of the specifications.) Submit for Approval: Students must submit their launch point, landing point, and height to Mrs. Vetter for approval. Students are not allowed to use the exact same launch/landing/height as another student so that each student in the class is creating their own unique fountain. You can get these approved by meeting with me before or after class, send an email, or send in a chat message on Teams.