Curriculum / Math / 9th Grade / Unit 8: Quadratic Equations and Applications / Lesson 10
Math
Unit 8
9th Grade
Lesson 10 of 15
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Graph and describe transformations to quadratic functions in mathematical and real-world situations.
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.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
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
In the Desmos activity, Will It Hit the Hoop?, watch the videos for Shots #2–4 on screens 5–7.
a. For each shot, predict if the ball will go in the basket. If you do not think it will go in the basket, name a transformation that could make it go in the basket.
b. Watch the videos on screens 20–22 to see the results of each shot. Were your predictions correct? Would the transformations you described make the ball go in the basket?
Will it Hit the Hoop? by is made available by Desmos. Copyright © 2017 Desmos, Inc. Accessed July 12, 2018, 5:28 p.m..
Given $${f(x)=2x^2-8x+12}$$, sketch the graph of $${f(x+4)-6}$$.
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
The graph of quadratic function $$f$$ below shows the path of a ball thrown. The $${y-}$$axis represents the vertical distance and the $${x-}$$axis represents the horizontal distance the ball has traveled. A wall is shown at $${x=5}$$ and has a height equal to $$2$$ units on the vertical axis.Â
Which of the following transformations is mostly likely to result in the ball clearing the wall? Select all that apply. Then explain your reasoning for each selection.Â
a.  $$f(x+4)$$
b.  $$f({x-}4)$$
c.  $$4f(x)$$
d.  $${1\over4}f(x)$$
e.  $$f(4x)$$
f.  $$f({1\over4}x)$$
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.
Lesson 9
Lesson 11
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
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
Write and analyze quadratic functions for revenue applications.
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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