Determining the Role of h and k in y = (x – h)2 + k
Course: MPM2D
Overall Expectation | Specific Expectations |
Relate transformations of the graph of y = x2 to the algebraic representation
y = a(x – h)2 + k. | Identify, through investigation using technology, the effect on the graph of y = x2 of transformations (i.e., translations, reflections in the x-axis, vertical stretches or compressions) by considering separately each parameter a, h, and k [i.e., investigate the effect on the graph of y = x2 of a, h, and k in y = x2 + k, y = (x – h)2, and y = ax2]. |
Explain the roles of a, h, and k in y = a(x – h)2 + k, using the appropriate terminology to describe the transformations, and identify the vertex and the equation of the axis of symmetry |
Learning Goals
- Determine the role of k in y = x2 + k
- Determine the role of h in y = (x – h)2
- Identify the vertex and equation of the axis of symmetry for y = (x – h)2 + k
Prior Knowledge Required
- Properties of y = x2
- How to determine the vertex and the equation of the axis of symmetry for a parabola
Minds-On - Project 3 parabolas
- Assign 1 of the parabolas to each group of 3 or 4 students
- Have students work in their small groups to identify the coordinates of the vertex and the equation of the axis of symmetry
- Have students come to the front of the class to label the projected parabolas
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Action Part 1 - In their small groups, have students use graph.tk to graph these parabolas:
- y = x2
- y = x2 + 2
- y = x2 + 5
- y = x2 – 3
- y = x2 – 1
- For each parabola, students must answer the following questions:
- How does the graph compare to y = x2?
- What are the coordinates of the vertex?
- What is the equation of the axis of symmetry?
- Students will use their results to answer the following questions:
- How can you use the equation to determine the transformation of y = x2?
- How can you use the equation to determine the coordinates of the vertex?
- Have students share their findings with the class
Part 2 - In their small groups, have students use graph.tk to graph the following parabolas:
- y = x2
- y = (x + 2)2
- y = (x + 5)2
- y = (x – 3)2
- y = (x – 1)2
- For each parabola, students must answer the following questions:
- How does the graph compare to y = x2?
- What are the coordinates of the vertex?
- What is the equation of the axis of symmetry?
- Students will use their results to answer the following questions:
- How can you use the equation to determine the transformation of y = x2?
- How can you use the equation to determine the coordinates of the verte?
- How can you use the equation to determine the equation of the axis of symmetry?
- Have students share their findings with the class
Part 3 - In their small groups, have students predict how the graph of y = (x – h)2 + k will compare to the graph of y = x2
- Based on their predictions, have students graph the following parabolas without using technology:
- y = (x – 2)2 + 3
- y = (x + 5)2 – 1
- Have students use graph.tk to verify their predictions
- Students must answer the following questions:
- How do h and k affect the graph (when you compare y = (x – h)2 + k to y = x2)?
- How can you use the equation to determine the coordinates of the vertex?
- How can you use the equation to determine the equation of the axis of symmetry?
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Consolidation - Have groups present their findings to the rest of the class
- As a class, create a document in Google Docs that outlines:
- How h affects the graph
- How k affects the graph
- How you can determine the coordinates of the vertex from the equation
y = (x – h)2 + k - How you can determine the equation of the axis of symmetry from the equation
y = (x – h)2 + k
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Assessment for Learning
- Do a Socrative quiz containing questions where students:
- Match an equation to its graph (and vice versa)
- Identify the coordinates of the vertex, given the equation
y = (x – h)2 + k - Identify the equation of the axis of symmetry, given the equation
y = (x – h)2 + k