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dered pairs. Conversely we have shown how to look at an equation of a parabola, re-write it in parent form if necessary, and then see the shapes of ordered pairs for both the given parabola and the parent parabola embedded in the equation. (We “connect” these two shapes with two small hori- zontal arrows in the middle of Figure 7.) These two shapes of ordered pairs enable us to uncover direc- tions for moving the given parabola to the parent parabola by following the order of operations in the ordered pairs’ coordinate expressions (see the sin- gle horizontal bold arrow in the middle of Fig- ure 7). Last Step. We leave you, the reader, with a challenge. We have shown that given an equation of a parabo- la in parent form we can uncover moving directions in the equation to write a program that moves the mystery parabola to the parent parabola. Referring to Problem 2, what might be a last step to sketch the given equation’s mystery parabola? More spe- cifically, your task is to sketch the graph of Y = 4( X − 3) 2 − 5 knowing that program Xshift −3| Yshift 5| Yscale (1/4) moves the graph of the mystery parabola to the parent parabola. Here is a hint: Develop an inverse program that will enable you to complete the task. This development will not only add the missing bold arrow in Figure 7, but will help you discover

Figure 7.

how the richness of our approach fits in nicely with integrating big ideas in mathematics like inverse motions (transformations and functions) and sym- metry.

Harold Mick Retired Faculty Virginia Tech mick@vt.edu

Benjamin Bazak Mathematics Teacher Patrick Henry High School bbazak@rcps.info

Virginia Mathematics Teacher vol. 44, no. 1

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