I start by writing the General Quadratic Function f(x)=ax^2+bx+c on the board. I like to use desmos for this activity because it is easy for students to set up sliders for the variables a, b, and c (see desmos_sliders) and explore by playing with parameters for the function. Graphing calculators work as well, but not as concretely as using a mouse to drag a slider.
For most of the Launch, I let students work with their partner to play with the parameters to determine which (a, b, or c) make the parabola open upward versus opening downward. Since students are exploring on their own, when it becomes time for students to share their responses, it is important to ask them to be as specific as possible when making observations:
My goal for the Launch is to guide students towards the understanding that positive values of parameter "a" will result in a parabola that opens upward; negative values of "a" will result in a parabola that opens downwards.
Today's closing activity, Graphing_Quadratics_Day 1_Close, was designed to quickly get a good sense of each student's proficiency with finding the vertex of a quadratic function. Students should work on this Exit Ticket individually on a half sheet of paper.
Part 2 of the activity asks students to explain, based on the equation, how they knew whether the parabola has a maximum or minimum value. When I review the students work, I will assess students use of structure (MP7) to understand the general shape of a graph.