Curriculum / Math / 9th Grade / Unit 8: Quadratic Equations and Applications / Lesson 13
Math
Unit 8
9th Grade
Lesson 13 of 15
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Write and analyze quadratic functions for revenue applications.
The core standards covered in this lesson
F.BF.A.1.B — Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
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.
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.
The foundational standards covered in this lesson
A.SSE.A.1 — Interpret expressions that represent a quantity in terms of its context 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.
A.SSE.B.3.A — Factor a quadratic expression to reveal the zeros of the function it defines.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
There is only one Anchor Problem for this lesson, as there is a lot to dig into with this one problem. Students can also spend an extended amount of time on independent, pair, or small-group practice working through applications from Lessons 11–13.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
A theater decided to sell special event tickets at $10 per ticket to benefit a local charity. The theater can seat up to 1,000 people, and the manager of the theater expects to sell all 1,000 seats for the event. To maximize the revenue for this event, a research company volunteered to do a survey to find out whether the price of the ticket could be increased without losing revenue. The results showed that for each $1 increase in ticket price, 20 fewer tickets will be sold.
Algebra I > Module 4 > Topic C > Lesson 23 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
A bakery sells small cakes for $${ {{$1}}0}$$ each. At this price, the bakery typically sells $${100}$$ cakes per week.Â
The owner of the bakery wants to increase the price of the cake in order to maximize revenue. She determines that for each $${{$1}}$$Â increase in price, she sells $$5$$ fewer cakes per week.Â
a. Which function represents the weekly revenue, $${R(x)}$$, the owner of the bakery can expect to earn from the cakes based on $$x$$ increases in price by $${{$1}}$$.
i.  $${R(x)}=(10-x)({100}+5x)$$
ii.  $${R(x)}=(10+x)({100}-5x)$$
iii.  $${R(x)}=(10-5x)({100}+x)$$
iv.  $${R(x)}=(10+5x)({100}-x)$$
b. At what price will the owner of the bakery earn the maximum weekly revenue from sales of the small cakes?
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.
Lesson 12
Lesson 14
Topic A: Deriving the Quadratic Formula
Describe features of the vertex form of a quadratic function and write quadratic equations in vertex form from graphs.
A.SSE.B.3 F.IF.B.4 F.IF.C.8
Complete the square.
A.SSE.B.3.B
Complete the square to identify the vertex and solve for the roots of a quadratic function.
A.REI.B.4.B A.SSE.B.3.B
Solve and interpret quadratic applications using the vertex form of the equation.
A.SSE.B.3.B F.IF.C.8.A
Convert and compare quadratic functions in standard form, vertex form, and intercept form.
F.IF.B.4 F.IF.C.9
Derive the quadratic formula. Use the quadratic formula to find the roots of a quadratic function.
A.REI.B.4.A
Determine the number of real roots of a quadratic function using the discriminant of the quadratic formula.
A.REI.B.4.B F.IF.C.7.A
Graph quadratic functions from all three forms of a quadratic equation.
F.IF.C.7.A
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Topic B: Transformations and Applications
Describe transformations to quadratic functions. Write equations for transformed quadratic functions.
F.BF.B.3
Graph and describe transformations to quadratic functions in mathematical and real-world situations.
Write and analyze quadratic functions for projectile motion and falling bodies applications.
A.CED.A.2 F.IF.C.8.A F.IF.C.9
Write and analyze quadratic functions for geometric area applications.
A.CED.A.2 F.IF.C.8.A
A.CED.A.2 F.BF.A.1.B F.IF.C.8.A
Solve and identify solutions to systems of quadratic and linear equations when two solutions are present.
A.REI.C.7 A.REI.D.11
Solve and identify solutions to systems of quadratic and linear equations when two, one, or no solutions are present.
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