![]() ![]() $$f\left(x\right)=\frac$$ must be the x-coordinate of the vertex.).We had an enjoyable time as a class looking through the solutions to third case and comparing the ways in which students wrote the equation, wondering what that might imply about different ways in which people went about finding the equation, and figuring out which were exact and which were approximate. The fact that students can use a guess-and-check approach, however, means that everyone has a way of making progress.Īll students did produce graphs that went through (or very, very, close to through) the points in first three cases (the ones where the vertex was given). Knowing how to graph a parabola, or solve a quadratic equation, or even understanding what effect all of the parameters in a quadratic equation in vertex form have on the the graph of the equation does not make it immediately obvious how to write an equation given three points, even when those points are specially chosen to eliminate the need to write three equations in three unknowns. If you think this would be a piece of cake for precalculus students with the background I’ve described, you would have been interested to hear the chorus of “That homework was so hard!” as students arrived to class on Friday. I told them they should feel free to stop working after 30 minutes, as long as they included thoughtful answers on the first two screens which required some writing. Students had a few minutes to start the activity in class on Thursday, and were asked to continue working through it for homework. In the first few cases, one of the points was the vertex, and in most of the others two of the points had the same y-coordinate. In the Desmos activity, the task was to enter an equation of a parabola that would go through a set of three points. If you’d like to try the activity yourself before reading on, you can do so here. ![]() A couple of months ago, they were successfully answering questions on tests asking them to find equations of power functions like these: These are intelligent people who have graphed plenty of parabolas and solved plenty of quadratic equations in Algebra 1 and 2, and have worked extensively this year with transformations of functions in general and transformations of power functions, exponential functions, and log functions in particular. I thoroughly enjoyed using an activity I created using Desmos Activity Builder over the course of the past couple of days with my precalculus students to help them think in new ways about quadratic functions.
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