For many years my grade 10 academic students have created parabolic art - a picture created using only parabolas. Students usually like this assignment as it gives them freedom to choose their design and allows those who might not be the most mathematically-inclined to shine. My perspective is that they cannot complete it without having a solid understanding of the transformation of quadratics.
After seeing some examples, they start by sketching their design on paper. Then they have to figure out the equations of each parabola. Most choose to use vertex form (y = a(x - h)^2 + k) and I tell them to estimate the 'a' value - (positive or negative? more or less than the previous equation?). I tell them that at least 95% of their equations will change along the way but they need a starting point for the next step.
Enter desmos.com. This marvelous, free on-line graphing software allows students to quickly and easily see graphs of their equations. They can find the intersection points of two parabolas and use that information to restrict the domains.
Here is the handout I give them. And here are some of this year's submissions. You will see that some students went a little crazy with a LOT of equations and some coloured in the final drawing too. My students are fantastic!