In this lesson, students make connections between vertex form of a parabola and transformations to an original function . Students begin by examining the graphs of two different parabolas and creating mathematical questions. They then create equations for those same parabolas in vertex form. As they compare the equations in vertex form with the transformations from an original equation, students leverage the structure of transformations and  of vertex form of a parabola (MP7). 

Next, students rewrite equations of a parabola from standard form to vertex form by completing the square. Rewriting the equation in vertex form allows students to see the transformations to the function directly from the equation without graphing.