Curriculum / Math / 9th Grade / Unit 8: Quadratic Equations and Applications / Lesson 9
Math
Unit 8
9th Grade
Lesson 9 of 15
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Lesson Notes
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Describe transformations to quadratic functions. Write equations for transformed quadratic functions.
The core standards covered in this lesson
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.
The foundational standards covered in this lesson
8.G.A.2 — Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
8.G.A.3 — Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Prior to this lesson, it may be helpful to recall and review the transformations that students studied in Unit 5, introduced using the absolute value function.
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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 $${f(x)=x^2}$$, where $$x$$ can be any real number.
Using a graphing calculator or other graphing technology, graph the function $$f$$ and each of the transformations to function $$f$$ shown below. For each graph, describe how the graph of each transformation compares to function $$f$$.
a. $$a(x)=f(x)+2$$
b. $$b(x)=-2f(x)$$
c. $$c(x)={1\over2} f(x)$$
d. $$d(x)=f(x+2)$$
e. $$e(x)=-f(x-2)-2$$
Building a quadratic function from f(x)=x^2, accessed on Aug. 18, 2017, 12:24 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.
Graphs of functions $${{{f(x)}}}$$ and $${{{{g(x)}} }}$$ are shown below. In each pair of graphs, the graph of function $${{{{g(x)}} }}$$ represents a transformation of function $${{{f(x)}}}$$.
A quadratic function $${{f(x)}}$$ is vertically stretched by a factor of $$3$$ and translated right by $$6$$ units.
Write an equation for $${h(x)}$$ to represent the transformation of the graph of function $${{f(x)}}$$ if
a. $${{f(x)}}=x^2$$
b. $${{f(x)}}=x^2-4$$
c. $${{f(x)}}=-(x-1)^2+2Â $$
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
Function $$f$$ is given by the equation $$f(x)=(x-2)^2+3$$.
Function $$g$$ is given by the equation $$g(x)=-(x+1)^2-1$$.
Describe the transformations that take the graph of $$f(x)$$ to the graph of $$g(x)$$.
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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Graph and describe transformations to quadratic functions in mathematical and real-world situations.
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
F.BF.B.3
Write and analyze quadratic functions for projectile motion and falling bodies applications.
A.CED.A.2F.IF.C.8.AF.IF.C.9
Write and analyze quadratic functions for geometric area applications.
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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