Understanding Quadratic Models (Graded)

Part 1: What does it mean for a quadratic to "model" a real-world situation? Can you think of any real-world business situations where a quadratic might be a more useful model than a linear function?

Part 2:What features of a quadratic did you focus on when thinking about business situations? The curvature? The slope? What does slope mean in this context even if you do not know how to calculate it at this point (look forward to calculus!)? How is a quadratic different from a line? How is a polynomial different from a line?

Part 3:But what happens if the solutions of your quadratic that you are trying to use are complex? That is, how do you feel about imaginary numbers? Do you think i is as much a number as ? In what way does i exist? Could it be a solution to a concrete business problem? Could a quadratic with complex solutions still model a concrete business situation?