Curriculum / Math / 11th Grade / Unit 2: Quadratics / Lesson 10
Math
Unit 2
11th Grade
Lesson 10 of 11
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Lesson Notes
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Describe features of quadratic functions in the context of a word problem. Evaluate and use function notation to describe contextual situations.
The core standards covered in this lesson
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.
The foundational standards covered in this lesson
A.CED.A.1 — Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
A.CED.A.2 — Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
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?
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?
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
What is the maximum area of a rectangle with a perimeter of 42 units?
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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Identify solutions to a system of a quadratic function and a linear function graphically and algebraically.
Topic A: Features of Quadratic Functions
Identify features of quadratic functions from equations and use these features to graph quadratic functions. Derive the equation of a parabola.
Standards
F.IF.C.7.AF.IF.C.8.AG.GPE.A.2
Identify the y-intercept and vertex of a quadratic function written in standard form through inspection and finding the axis of symmetry. Graph quadratic equations on the graphing calculator.
F.IF.C.7.AF.IF.C.8.A
Write a quadratic equation in intercept form by factoring. Describe the features of a quadratic function written in intercept form.
A.SSE.A.2A.SSE.B.3.AF.IF.C.8.A
Transform a quadratic function in vertex form. Describe the domain, range, and intervals where the function is increasing and decreasing.
F.BF.B.3F.IF.B.4F.IF.C.9
Solve quadratic equations written in vertex form and describe graphical features from vertex form.
A.REI.A.1A.REI.B.4.B
Complete the square to convert an equation written in standard form to an equation written in vertex form.
A.REI.B.4.BA.SSE.B.3.B
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Topic B: Imaginary Solutions and Operating with Complex Numbers
Identify solutions that are non-real from a graph and an equation using the discriminant. Define imaginary and complex numbers.
A.REI.B.4.BN.CN.A.1N.CN.C.7
Add, subtract, and multiply complex numbers.
N.CN.A.1N.CN.A.2
Topic C: Applications, Systems, and Inverse with Quadratics
Compare, analyze, and solve quadratic functions in projectile motion application problems.
F.BF.A.1F.BF.B.3F.IF.B.6F.IF.C.8.AF.IF.C.9
F.BF.A.1F.IF.B.6F.IF.C.8.AF.IF.C.9
A.REI.A.1A.REI.C.7A.REI.D.11
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