Quadratic Function Applications

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Objective

SWBAT solve real world scenarios using quadratic functions.

Big Idea

Students will interpret the components of a quadratic function to solve for missing values.

Do-Now

10 minutes

Students will complete the Do Now in 5 minutes. As students are working I will pass back the graded exit cards from our last class. Two student student volunteers will then go up to the board to sketch their Do-Now responses, carefully labeling the key elements of the graph.

A student volunteer will read our objective, "SWBAT solve real world scenarios using quadratic functions."

I will ask the class to generate real world situation and scenarios that could be solved using a quadratic function. I will ask students to support their statements with a quick sketch on the board. Lastly, we will briefly review the old exit cards as a whole group.

Guided Practice

20 minutes

Students will use quadratic functions to model the scenarios depicted with these Examples. We will solve Example One and Three as a whole group. Students will work with a neighbor to solve Example Two.

By this point in the year my students will be very familiar with solving word problems. The shift in today's lesson require students to visualize the graph of a quadratic function and use its key elements to represent what is happening in each scenario. This process will be supported with a sketch of each function. The sketch can be completed by hand, or with a graphing calculator. My students were better able to work through each problem when they were able to see the question and work side-by-side. I will leave each prompt frozen on the screen, and will complete my think aloud and draw any corresponding sketches by hand on a whiteboard. 

After we complete each example, I will ask student volunteers to explain and justify their responses in great detail. The reflection component of this lesson is very important, and should move at a deliberately slow pace. Students also found it helpful when we defined what our x and y values represented at the start of each problem.

Partner Practice

40 minutes

The class will apply the strategies that they have learned to practice solving word problems that involve Quadratic Functions. Students can work individually or a homogeneous pairs to complete this assignment. They will also be encouraged to use the graphing calculator to support and justify their responses.

Students will likely need the most support with Question Four. I will encourage students to make an attempt to solving or sketch this problem, but this will be reviewed as a whole group towards the end of class.

After 20 minutes, I will divide the students into 4-6 groups. I will then ask each group to use a sheet of chart paper to display, diagram, and solve one Example from this assignment. Each group will then come to the front of the room to lead the class through discussion of each response.

Closing

10 minutes

I will end our class today by giving students a brief summary of what's to come regarding Quadratic Functions in future units. I will then ask a few student volunteers to summarize our study of Quadratics, and to discuss their major takeaways. Students will then complete an Exit Card.