Curriculum / Math / 9th Grade / Unit 8: Quadratic Equations and Applications / Lesson 11
Math
Unit 8
9th Grade
Lesson 11 of 15
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Lesson Notes
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Write and analyze quadratic functions for projectile motion and falling bodies applications.
The core standards covered in this lesson
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.
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.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
Students had a brief introduction to quadratic applications in Lesson 13 of Unit 7, and in Lesson 4 of this unit, students interpreted quadratic functions using the vertex form. In Lessons 11–13 of this unit, students delve into writing and analyzing applications of quadratic functions at a deeper level. In each application problem, students will use their understanding of quadratic functions to interpret key features in context. For example, students will solve for the roots and determine what the value of the roots mean in projectile motion problems, area problems, and revenue applications.
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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
Suppose $${h(t)=-5t^2+10t+3}$$ is the height of a diver above the water (in meters), $$t$$ seconds after the diver leaves the springboard.
Springboard Dive, accessed on Aug. 18, 2017, 2:42 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
Chris stands on the edge of a building at a height of 60 feet. and throws a ball upward with an initial velocity of 68 feet per second. The ball eventually falls all the way to the ground.
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
15-20 minutes
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
5-10 minutes
A softball player throws a ball with an initial velocity of 26 feet per second. The ball leaves her hand at 3 feet above the ground.
At the same time, her softball coach throws a ball with an initial velocity of 32 feet per second. The ball leaves her hand at 2 feet above the ground.
Whose ball takes longer to land on the ground after being thrown? By approximately how many seconds? Give your answer to the nearest tenth of a second.Â
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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Write and analyze quadratic functions for geometric area applications.
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.
Standards
A.SSE.B.3F.IF.B.4F.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.BA.SSE.B.3.B
Solve and interpret quadratic applications using the vertex form of the equation.
A.SSE.B.3.BF.IF.C.8.A
Convert and compare quadratic functions in standard form, vertex form, and intercept form.
F.IF.B.4F.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.BF.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.
A.CED.A.2F.IF.C.8.AF.IF.C.9
A.CED.A.2F.IF.C.8.A
Write and analyze quadratic functions for revenue applications.
A.CED.A.2F.BF.A.1.BF.IF.C.8.A
Solve and identify solutions to systems of quadratic and linear equations when two solutions are present.
A.REI.C.7A.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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