Curriculum / Math / 11th Grade / Unit 2: Quadratics / Lesson 3
Math
Unit 2
11th Grade
Lesson 3 of 11
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Lesson Notes
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Write a quadratic equation in intercept form by factoring. Describe the features of a quadratic function written in intercept form.
The core standards covered in this lesson
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.
A.SSE.A.2 — Use the structure of an expression to identify ways to rewrite it. For example, see x<sup>4</sup> — y<sup>4</sup> as (x²)² — (y²)², thus recognizing it as a difference of squares that can be factored as (x² — y²)(x² + y²).
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 will require students to organize notes so they are able to easily see and access relevant information while studying. Students should annotate the equation with the ways they can find each of the features of the quadratic equation.
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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
Below is a quadratic equation.
$${g(x)=4x^2+7x-15}$$
What are the roots, vertex, and y-intercept of this function?
Which equation matches with which graph? How do you know?
$${f(x)=-4x^2+8x-16}$$
$${g(x)=-4x^2+16}$$
Graph A
Graph B
Graph C
Graph D
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Find the roots by factoring each of the following quadratic equations.Â
Additionally, for each equation, identify:Â
Â
a. Â Â $${3x^2-27=0}$$
b. Â Â $${2x^2+7x-15=0}$$
c. Â Â $${4x^2-10x+25=0}$$
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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Transform a quadratic function in vertex form. Describe the domain, range, and intervals where the function is increasing and decreasing.
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.
Standards
F.IF.C.7.AF.IF.C.8.AG.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.
F.IF.C.7.AF.IF.C.8.A
A.SSE.A.2A.SSE.B.3.AF.IF.C.8.A
F.BF.B.3F.IF.B.4F.IF.C.9
Solve quadratic equations written in vertex form and describe graphical features from vertex form.
A.REI.A.1A.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.BA.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.BN.CN.A.1N.CN.C.7
Add, subtract, and multiply complex numbers.
N.CN.A.1N.CN.A.2
Topic C: Applications, Systems, and Inverse with Quadratics
Compare, analyze, and solve quadratic functions in projectile motion application problems.
F.BF.A.1F.BF.B.3F.IF.B.6F.IF.C.8.AF.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.1F.IF.B.6F.IF.C.8.AF.IF.C.9
Identify solutions to a system of a quadratic function and a linear function graphically and algebraically.
A.REI.A.1A.REI.C.7A.REI.D.11
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