Unlocking Vertex Form: Graphing Quadratic Functions Like a Pro

Algebra 2 Grades High School 10:18 Video
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Lesson Description

Master graphing quadratic functions in vertex form. Learn to identify the vertex, create a table of values using symmetry, and accurately plot the parabola. Perfect for Algebra 2 students!

Video Resource

Graphing Quadratic Functions Algebra 2 | Vertex Form

Kevinmathscience

Duration: 10:18
Watch on YouTube

Key Concepts

  • Vertex Form of a Quadratic Equation
  • Vertex Identification (h, k)
  • Symmetry of Parabolas
  • Table of Values

Learning Objectives

  • Students will be able to identify the vertex of a quadratic function given in vertex form.
  • Students will be able to create a table of values using the vertex and symmetry to plot points on a quadratic function.
  • Students will be able to accurately graph a quadratic function given its vertex form equation.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the standard form of a quadratic equation and contrasting it with the vertex form. Briefly discuss the advantages of vertex form in identifying the vertex of the parabola. Show the video (https://www.youtube.com/watch?v=AkHCKDvtA4M) and ask students to follow along, noting key steps.
  • Vertex Identification (10 mins)
    Explain how the values 'h' and 'k' in the vertex form equation, y = a(x - h)^2 + k, directly correspond to the x and y coordinates of the vertex. Emphasize the sign change for 'h' (x-coordinate). Work through several examples, having students identify the vertex from given equations.
  • Creating a Table of Values Using Symmetry (15 mins)
    Demonstrate the process of creating a table of values with the vertex in the middle. Explain the concept of symmetry and how it allows us to find corresponding y-values efficiently. Walk through an example, calculating y-values for x-values around the vertex and using symmetry to complete the table.
  • Graphing the Quadratic Function (10 mins)
    Show students how to plot the points from the table of values onto a coordinate plane. Guide them in drawing a smooth curve through the points to create the parabola. Discuss the axis of symmetry and its relationship to the vertex.
  • Practice and Application (10 mins)
    Provide students with several vertex form equations and have them independently identify the vertex, create a table of values, and graph the quadratic function. Circulate to provide assistance and answer questions.

Interactive Exercises

  • Vertex Form Matching Game
    Provide students with cards containing vertex form equations and corresponding cards with the vertex coordinates. Students must match the equations to their correct vertex. (Can be done individually or in pairs).
  • Graphing Challenge
    Divide students into small groups and give each group a different vertex form equation. Groups must work together to graph the function accurately on a large sheet of paper. The group with the most accurate and well-labeled graph wins.

Discussion Questions

  • How does the vertex form of a quadratic equation make it easier to find the vertex compared to the standard form?
  • Why is the concept of symmetry important when graphing quadratic functions?
  • How do the 'h' and 'k' values in the vertex form equation affect the position of the parabola on the coordinate plane?

Skills Developed

  • Algebraic Manipulation
  • Graphing Skills
  • Problem-Solving
  • Analytical Thinking

Multiple Choice Questions

Question 1:

What is the vertex of the quadratic function y = (x - 3)^2 + 5?

Correct Answer: (3, 5)

Question 2:

In the vertex form equation y = a(x - h)^2 + k, which variable represents the y-coordinate of the vertex?

Correct Answer: k

Question 3:

If a quadratic function in vertex form has a vertex at (2, -1), what is the equation of the axis of symmetry?

Correct Answer: x = 2

Question 4:

Which direction does the graph of y = -(x + 1)^2 - 4 open?

Correct Answer: Downwards

Question 5:

The vertex form of a quadratic equation is given by y = a(x - h)^2 + k. What does the 'a' value determine about the parabola?

Correct Answer: Whether the parabola opens up or down and its width

Question 6:

What transformation does the '+3' in the equation y = (x+3)^2 represent?

Correct Answer: A shift to the left by 3 units

Question 7:

Which point on the parabola is also on the axis of symmetry?

Correct Answer: Vertex

Question 8:

How can you use symmetry to easily create a table of values for a quadratic function in vertex form?

Correct Answer: Both A and B

Question 9:

Which of the following equations is in vertex form?

Correct Answer: y = a(x - h)^2 + k

Question 10:

What is the effect of changing the 'k' value in the vertex form y = a(x - h)^2 + k?

Correct Answer: It shifts the parabola vertically

Fill in the Blank Questions

Question 1:

The vertex form of a quadratic equation is y = a(x - h)^2 + k, where (h, k) represents the ______ of the parabola.

Correct Answer: vertex

Question 2:

The axis of _______ is a vertical line that passes through the vertex of a parabola.

Correct Answer: symmetry

Question 3:

If the 'a' value in the vertex form is negative, the parabola opens ____.

Correct Answer: downward

Question 4:

In the vertex form, y = (x + 2)^2 - 3, the graph shifts 2 units to the ______.

Correct Answer: left

Question 5:

The _______ of a parabola are symmetrical with respect to the axis of symmetry.

Correct Answer: points

Question 6:

To create a table of values, place the coordinates of the _______ in the middle of the table.

Correct Answer: vertex

Question 7:

The value of 'h' in the vertex form equation gives the ________ coordinate of the vertex.

Correct Answer: x

Question 8:

In vertex form, a change in the 'k' value results in a ________ shift of the graph

Correct Answer: vertical

Question 9:

If the vertex of a parabola is (5,0), then the axis of symmetry is x = ____

Correct Answer: 5

Question 10:

For the equation y=2(x-1)^2+4, the y-coordinate of the vertex is _______.

Correct Answer: 4

Educational Standards

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. A2.F.1.2:Identify the parent forms of exponential, radical (square root and cube root only), quadratic, and logarithmic functions. Predict the effects of transformations [𝑓(𝑥 + 𝑐), 𝑓(𝑥) + 𝑐, 𝑓(𝑐𝑥), and 𝑐𝑓(𝑥)] algebraically and graphically.

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