## Task

Emery graphs the function $f$ given by $f(x) = (x-1)(x+2)(x-50)$ on his graphing calculator and gets the following graph.

He says "so, it's an upside down parabola."

- Experiment with the viewing window to decide if Emery is correct.
- Explain how you could choose a viewing window in advance that shows the main features of the graph.

## IM Commentary

The purpose of this task is to give students an opportunity to see and use the structure of the factored form of a polynomial (MP7). The factor $x-50$ tells them that they should include $x=50$ in the range on the $x$-axis. Students might also draw on their knowledge of the long run behavior of a cubic polynomial to recognize that Emery's graph must eventually return across the $x$-axis to the right of his current viewing window.