The ANCIENT method is to use graph paper to get a visual representation of a function. I used to use this method to teach the skill of graphing lines in Algebra 1. I typically do not spend too much time in my Algebra 2 class using the paper and pencil method because the goal is to understand how the transformation form (vertex form) changes the parent function. Using paper and pencil is so time consuming and I really struggle to wait for students to use it (especially when they all love to use rulers)
Emily is in her fourth year teaching mathematics at Perry Meridian High School. She graduated from Eastern Michigan University in 2000 with a BS degree in Mathematics and in 2006 with a MS in Sports Administration. In the summer of 2013, she earned a trainer endorsement with NMSI (National Math and Science Initiative). You can visit Emily's blog Crazy in Math for more great ideas or follow her on Twitter @esteiner51.