Quadratics

Lesson 10

Math

Unit 2

11th Grade

Lesson 10 of 11

Objective


Describe features of quadratic functions in the context of a word problem. Evaluate and use function notation to describe contextual situations.

Common Core Standards


Core Standards

  • F.BF.A.1 — Write a function that describes a relationship between two quantities Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
  • F.IF.B.6 — Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
  • F.IF.C.8.A — Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
  • F.IF.C.9 — Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

Foundational Standards

  • A.CED.A.1
  • A.CED.A.2

Criteria for Success


  1. Use a quadratic equation to model a quadratic situation. 
  2. Describe the features of a quadratic equation that can be defined with a contextual situation. 
  3. Write quadratic equations that model situations where profit or area needs to be maximized.
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Anchor Problems


Problem 1

Jaden is selling tickets to a show his band is headlining. He knows from ticket sales for the last few shows they have done that their profits can be modeled by the function $${P(x)=-{1\over16}x^2+24x+20}$$, where $$P$$ is the profit and $$x$$ is the number of tickets sold.

 

How many tickets should Jaden sell so that he gets the maximum profit? What is that profit? What is the profit per ticket at this rate?

Guiding Questions

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Problem 2

A family wants to fence in their yard and got 180 feet of fencing from a friend to do this project. 

A diagram of their house and a sketch of the shape of the yard they want to fence in is shown below. The family is going to use the side of the house as one side of the yard. 

What are the dimensions of the yard that will give them the greatest fenced in area?

Guiding Questions

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Target Task


What is the maximum area of a rectangle with a perimeter of 42 units?

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

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Lesson 9

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Lesson 11

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Features of Quadratic Functions

Topic B: Imaginary Solutions and Operating with Complex Numbers

Topic C: Applications, Systems, and Inverse with Quadratics

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