Lesson plan 5.1 Stretching/Reflecting Quadratic Relations
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Subject:MPM2D MATHEMATICS |
Grade: 10 |
Lesson No: 5.1 |
Duration: 3 hours |
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Unit 5 - Applying Quadratic Models |
Topic: 5.1 Stretching/Reflecting Quadratic Relations |
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Overall Expectations (Directly from The Ontario Curriculum) |
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• determine the basic properties of quadratic relations; • relate transformations of the graph of y = x2 to the algebraic representation y = a(x – h) 2 + k; • solve quadratic equations and interpret the solutions with respect to the corresponding relations; • solve problems involving quadratic relations |
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Specific Expectations (Directly from The Ontario Curriculum) |
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– 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; Quadratic Relations of the Form y ax2 = + bx + c Relating the Graph of y = Transformations x2 and Its 48 THE ONTARIO CURRICULUM, GRADES 9 AND 10: MATHEMATICS – sketch, by hand, the graph of y = a(x – h ) 2 + k by applying transformations to the graph of y = x2 [Sample problem: Sketch the graph of y = – (x – 3)2 + 4, and verify using technology.]; – determine the equation, in the form y = a(x – h) 2 + k, of a given graph of a parabola. |
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Learning Goals |
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Today you will Examine the effect of the parameter a in the equation Y=ax2 on the graph of the equation. |
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Success Criteria |
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By the end of class: - I can Stretching/Reflecting Quadratic Relations. |
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Materials and Resources |
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- Graphing calculator and/or graph paper - Laptop with Internet access |
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Lesson Structure and Activities |
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Timing |
Lesson |
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~10 minutes ~20 minutes ~20 minutes ~60 minutes ~60 minutes ~10 minutes
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1. Students to Read Lesson Plan 2. Students to Study Glossary 3. Students to complete Warmer Question 4. Students to study Lesson 5. Students to complete Assignment 6. Students to complete Exit card
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