This is a handout that can be used as a way to introduce quadratic functions. It starts with a real world connection that the students can understand and literally see in their mind before they even graph on their paper. The teacher guides the students through the set up and breaking down of the problem to finally see the quadratic that they pictured in their mind form on their paper. It's a great way to start because the students discover for themselves (with teacher guidance) what a quadratic is and how it relates to real life. It's a way of introducing something new to the students so that they can make connections and so that it will always make sense.
Page two goes on to show the parent function for quadratics -also a necessary part of starting off learning about quadratics and making connections later on.