Shading the Solution: Graphing Quadratic Inequalities

Algebra 2 Grades High School 23:34 Video
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Lesson Description

Learn how to graph quadratic inequalities in standard form, including identifying the vertex, creating a table of values, determining solid vs. dashed lines, and shading the correct region.

Video Resource

Graphing Quadratic Inequalities Algebra | Standard Form

Kevinmathscience

Duration: 23:34
Watch on YouTube

Key Concepts

  • Quadratic inequalities in standard form
  • Vertex of a parabola
  • Table of values for graphing
  • Solid vs. dashed lines for inequalities
  • Shading above or below the parabola based on the inequality sign

Learning Objectives

  • Students will be able to identify the vertex of a quadratic inequality in standard form.
  • Students will be able to construct a table of values to accurately graph a quadratic inequality.
  • Students will be able to determine whether to use a solid or dashed line when graphing a quadratic inequality.
  • Students will be able to shade the correct region (above or below the parabola) to represent the solution set of a quadratic inequality.

Educator Instructions

  • Introduction (5 mins)
    Briefly review the concepts of quadratic functions and inequalities. Introduce the idea of graphing quadratic inequalities and explain that the solution is a region on the coordinate plane.
  • Video Viewing and Note-Taking (15 mins)
    Play the 'Graphing Quadratic Inequalities Algebra | Standard Form' video by Kevinmathscience. Instruct students to take notes on the key steps involved in graphing quadratic inequalities: finding the vertex, creating a table of values, deciding on solid or dashed lines, and determining which region to shade. Emphasize the 'crocodile mouth' analogy for understanding inequality symbols.
  • Guided Practice (20 mins)
    Work through 2-3 example problems together as a class. For each problem, follow these steps: 1. Rewrite the inequality as an equation to find the vertex. 2. Create a table of values. 3. Graph the parabola (solid or dashed). 4. Use the inequality to determine whether to shade above or below the parabola. 5. Clearly shade the solution region.
  • Independent Practice (15 mins)
    Assign students 2-3 similar problems to work on independently. Circulate the classroom to provide assistance as needed.
  • Wrap-up and Assessment (5 mins)
    Review the key concepts and answer any remaining questions. Announce the multiple choice and fill in the blank quiz for assessment.

Interactive Exercises

  • Desmos Activity
    Use a Desmos activity where students can manipulate the coefficients of a quadratic inequality and observe how the graph changes. This will allow them to visualize the effect of each parameter on the parabola's position and shading.

Discussion Questions

  • How does the inequality symbol determine whether you use a solid or dashed line?
  • What does it mean to 'shade above' or 'shade below' a parabola?
  • How can you check if you've shaded the correct region?
  • Why is the vertex important when graphing a quadratic inequality?

Skills Developed

  • Graphing quadratic functions
  • Interpreting inequalities
  • Problem-solving
  • Analytical thinking

Multiple Choice Questions

Question 1:

Which of the following is the first step in graphing a quadratic inequality in standard form?

Correct Answer: Find the vertex of the related quadratic equation.

Question 2:

How does the inequality symbol ≤ affect the graph of a quadratic inequality?

Correct Answer: It indicates a solid line and shading below the parabola.

Question 3:

The vertex of the parabola represented by the equation y = x^2 - 4x + 5 is:

Correct Answer: (2, 1)

Question 4:

If the inequality is y > x^2 + 2x - 3, which region should be shaded?

Correct Answer: Above the parabola.

Question 5:

What type of line is used when graphing y < x^2?

Correct Answer: Dashed line.

Question 6:

The table of values in a quadratic inequality is based on what?

Correct Answer: Symmetry

Question 7:

Where is the vertex located on a quadratic inequality?

Correct Answer: The graph turns

Question 8:

A vertex formula is known as:

Correct Answer: -b/2a

Question 9:

When shading y is smaller, you shade:

Correct Answer: Below

Question 10:

When shading y is bigger, you shade:

Correct Answer: Above

Fill in the Blank Questions

Question 1:

The point where the graph turns is known as the _________.

Correct Answer: vertex

Question 2:

If the inequality symbol includes an 'equal to' component (≤ or ≥), the parabola should be graphed as a ________ line.

Correct Answer: solid

Question 3:

To graph a quadratic inequality, the initial steps are the same as graphing a regular quadratic _________.

Correct Answer: equation

Question 4:

The formula x = -b/2a is used to find the x-coordinate of the _________.

Correct Answer: vertex

Question 5:

When graphing y > x^2, you shade ________ the parabola.

Correct Answer: above

Question 6:

The _______ is the main portion of the graph we can see the y values on.

Correct Answer: y-axis

Question 7:

A _______ line means that there is no line at the bottom.

Correct Answer: dashed

Question 8:

The first step is to always find the _______.

Correct Answer: vertex

Question 9:

The next step to do after finding the vertex is to make a _______.

Correct Answer: table

Question 10:

If the _______ eats the y, then you will shade above.

Correct Answer: crocodile

Educational Standards

A2.A.1.9:Solve systems of linear inequalities in two variables, with a maximum of three inequalities; graph and interpret the solutions on a coordinate plane. Graphing calculators or other appropriate technology may be used. A2.F.1.3:Graph a quadratic function. Identify the domain, range, x- and y-intercepts, maximum or minimum value, axis of symmetry, and vertex using various methods and tools that may include a graphing calculator or appropriate technology.

Teaching Materials

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