Curriculum / Math / 11th Grade / Unit 2: Quadratics / Lesson 9
Math
Unit 2
11th Grade
Lesson 9 of 11
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Compare, analyze, and solve quadratic functions in projectile motion application problems.
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.BF.B.3 — Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
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
Suggestions for teachers to help them teach this lesson
This lesson reviews projectile motion contexts from Algebra 1.Â
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Below are two quadratic functions with some additional information shown. Compare the features shown below.
$${f(x)}$$
The function $${g(x)}$$ has a vertical stretch of $${-2}$$.
The equation below expresses the approximate height, h, in meters of a ball, t seconds after it is launched from a pitching machine 3 feet off the ground with an initial velocity of v meters per second. If the batter doesn’t hit the ball, the ball will hit the ground in 8 seconds. What was the initial velocity of the ball?
$${h(t)=-4.9t^2+vt+3}$$
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Suppose Brett and Andre each throw a baseball into the air. The height of Brett's baseball is given by
$${h(t)=-16t^2+79t+6}$$
where $$h$$ is in feet and $$t$$ is in seconds. The height of Andre's baseball is given by the graph below.
Brett claims that his baseball went higher than Andre’s, and Andre says that his baseball went higher.Â
Throwing Baseballs, accessed on Aug. 18, 2017, 2:52 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.
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 8
Lesson 10
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.
F.IF.C.7.A F.IF.C.8.A G.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.Â
F.IF.C.7.A F.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.2 A.SSE.B.3.A F.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.3 F.IF.B.4 F.IF.C.9
Solve quadratic equations written in vertex form and describe graphical features from vertex form.Â
A.REI.A.1 A.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.B A.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.B N.CN.A.1 N.CN.C.7
Add, subtract, and multiply complex numbers.
N.CN.A.1 N.CN.A.2
Topic C: Applications, Systems, and Inverse with Quadratics
F.BF.A.1 F.BF.B.3 F.IF.B.6 F.IF.C.8.A F.IF.C.9
Describe features of quadratic functions in the context of a word problem. Evaluate and use function notation to describe contextual situations.
F.BF.A.1 F.IF.B.6 F.IF.C.8.A F.IF.C.9
Identify solutions to a system of a quadratic function and a linear function graphically and algebraically.
A.REI.A.1 A.REI.C.7 A.REI.D.11
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