Curriculum  /  Math  /  11th Grade  /  Unit 2: Quadratics  /  Lesson 2

Quadratics

Lesson 2

Math

Unit 2

11th Grade

Lesson 2 of 11

Objective

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.

Common Core Standards

Core Standards

  • F.IF.C.7.A — Graph linear and quadratic functions and show intercepts, maxima, and minima.
  • 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.

Foundational Standards

  • A.APR.A.1
  • F.BF.B.3
  • A.SSE.B.3

Criteria for Success

  1. Describe the features that you can “see” in standard form and intercept form. 
  2. Calculate the vertex of a function represented in standard form by using $${-b\over{2a}}$$.
  3. Identify the vertex of the function by knowing that the parabola is symmetrical around the vertex and then using the x-coordinate of the vertex to find the y-coordinate of the vertex. 
  4. Identify the y-intercept of the function in intercept form by finding the constant value.
  5. Describe the purpose of using graphing calculators in Algebra 2. 
  6. Use [Y=] and [GRAPH] to graph quadratic functions.
  7. Use [WINDOW] to adjust the viewing window. Adjust the scaling factor.
  8. Use [Zoom] "0. ZoomFit" as well as other “Zoom” options to show quadratic.
  9. Describe how the [CALC] and [TRACE] functions can be used to find features of quadratic functions on the graphing calculator. 

Tips for Teachers

  • This lesson is the first in which graphing calculators are introduced. 
  • This lesson may need to be split into two so you can adequately introduce the graphing calculator. 
  • While Desmos is an invaluable tool that we will also use from this point forward, graphing calculators are essential tools for students to understand how to use for AP Calculus and other senior-level math courses as well as some college-level math. 
  • The TI Connect CE software and the USB cable will be invaluable tools to allow for you to develop problem sets using graphing calculator screens.
  • This lesson provides an opportunity to discuss how to show work when a graph is produced on technology or information is determined from technology. Ensure there is common understanding of what students need to record to show evidence of learning. 
  • 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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Anchor Problems

25-30 minutes

Problem 1

Graph the following quadratic equation in your graphing calculator.

$${y=2x^2-4x+9}$$

Guiding Questions

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Problem 2

Below is a quadratic equation written in standard form. 

$${y=2x^2-4x+9}$$

And this is the graph of the quadratic equation on a graphing calculator. 

  • What do you need to change on the graphing calculator so you can “see” the y-intercept? 
  • How can you use both the [ZOOM] and [WINDOW] features on the calculator to see this? 
  • What options within the [CALC] feature will allow you to find the y-intercept? 

Guiding Questions

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Problem 3

Part A

Find the vertex of the quadratic equation using the graphing calculator.

$${y=2x^2-4x+9}$$

  • Alter the window so you can more clearly see the vertex. 
  • Use the [CALC] feature to determine the minimum value. 

Part B

The formula $${-b\over2a}$$ can be used to find the axis of symmetry of the quadratic function. Use this to verify the vertex you found in the graphing calculator. 

Guiding Questions

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Target Task

5-10 minutes

Below is a quadratic equation in standard form and the associated graph and window settings. 

  1. Find the vertex and the y-intercept algebraically. 
  2. Describe how you would find the vertex and the y-intercept on the graphing calculator. 
  3. Describe how you could adjust the graph so that the vertex, roots, and y-intercept are shown. 

Next

Write a quadratic equation in intercept form by factoring. Describe the features of a quadratic function written in intercept form.

Lesson 3
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Features of Quadratic Functions

Topic B: Imaginary Solutions and Operating with Complex Numbers

Topic C: Applications, Systems, and Inverse with Quadratics

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