Curriculum / Math / 9th Grade / Unit 8: Quadratic Equations and Applications / Lesson 8
Math
Unit 8
9th Grade
Lesson 8 of 15
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Lesson Notes
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Graph quadratic functions from all three forms of a quadratic equation.
The core standards covered in this lesson
F.IF.C.7.A — Graph linear and quadratic functions and show intercepts, maxima, and minima.
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
This lesson connects back to Lesson 5, where students compared and converted between the three forms of a quadratic equation. Having learned the quadratic formula in Lesson 6, students now have an additional strategy to find the roots from standard form.Â
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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
A quadratic function is represented in three different equation forms. For each feature listed, either give the value that is revealed by the equation’s form or briefly explain how you would determine the value.
Then use the information to graph the quadratic function.
Graph each quadratic function. For each function, identify the vertex, the root(s), the $${y-}$$intercept, and the axis of symmetry.
a. $${f(x)=(x-5)(x-1)}$$
b. $${g(x)={1\over2}x^2+5x+6}$$
c. $${h(x)=-(x-3)^2+4}$$
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
Two quadratic functions are given below.
$${j(x)=(x-4)(x+2)}$$
$${k(x)=-(x-1)^2-9}$$
Sketch and compare the graphs of the two functions. How are they similar? How are they different?
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.
Next
Describe transformations to quadratic functions. Write equations for transformed quadratic functions.
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
F.IF.C.7.A
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Topic B: Transformations and Applications
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.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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