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Transformations of quadratic functions
- Lesson: 15:11
- Lesson: 1a5:11
- Lesson: 2a9:47
- Lesson: 2b10:27
Transformations of quadratic functions
Related Concepts: Transformations of functions: Horizontal translations, Transformations of functions: Vertical translations, Reflection across the y-axis: y=f(−x), Reflection across the x-axis: y=−f(x)
Lessons
- 1.Reflection in the x-axis
Reflect a quadratic function in the x-axis:a)Sketch the following functions on the same set of coordinate axes:
y=x2 VS. −y=x2b)Compared to the graph of y=x2, the graph of −y=x2 is a reflection in the _______________ . - 2.Compared y=x2 to basic quadratic function:
i) describe every step of transformations
ii) use transformation concepts to sketch the functiona)y=2(x−3)2−8b)y=−31(x+5)2+4
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14.
Quadratic Functions
14.1
Characteristics of quadratic functions
14.2
Transformations of quadratic functions
14.3
Quadratic function in general form: y=ax2+bx+c
14.4
Quadratic function in vertex form: y = a(x−p)2+q
14.5
Completing the square
14.6
Converting from general to vertex form by completing the square
14.7
Shortcut: Vertex formula
14.8
Graphing parabolas for given quadratic functions
14.9
Finding the quadratic functions for given parabolas
14.10
Applications of quadratic functions