Graphing Quadratic Functions Day 1

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Objective

SWBAT graph a quadratic function by finding the axis of symmetry and vertex as their starting points.

Big Idea

The idea of symmetry can be used to graph quadratic functions in the coordinate plane.

Launch

5 minutes

To begin today's lesson, I ask students to work with a partner on the Launch Activity.  I will have my students use either a graphing calculator or the desmos.com online calculator for this activity.

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:

  • What coefficients did you try?
  • How did each coefficient affect the appearance of the graph?
  • Which coefficient was responsible for changing the orientation of the graph? 

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.

Direct Instruction

30 minutes

Closure

5 minutes

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.