transformations of quadratic functions section 2.1 beginning on page 48
TRANSCRIPT
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Transformations of Quadratic Functions
Section 2.1 beginning on page 48.
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The Big IdeasIn this section we will learn about….
• Describing transformations of quadratic functions (extension of section 1.2)
o Translations (horizontal and vertical)o Reflections (in the x-axis and the y-axis)o Stretches and Shrinks (horizontal and vertical)
• Writing transformations of quadratic functions.
o NEW: Writing transformed quadratic functions in vertex form. o Writing transformed quadratic functions, applying transformations one at
a time. (extension of section 1.2)
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Core Vocabulary
Previously Learned:
• Transformations
New Vocabulary:
• Quadratic Function• Parabola• Vertex of a Parabola• Vertex Form
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Quadratic FunctionsA quadratic function is a function that can be written in the form where .
The U-shaped graph of a quadratic function is called a parabola.
In the previous chapter we graphed quadratic functions using tables of values. In this section we will learn to graph quadratic functions using the transformations to the parent function .
(Why can’t a=0 ? )
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Translations
Describe each transformation:
1) 2) 3) 4)
Translation 4 units left
Translation 3 units right
Translation 1 unit up Translation 2 units down
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Translations
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Reflections
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Stretches and Shrinks
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Transformations of Quadratic Functions
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Vertex Form** This is new and important, put this in your notes **
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Writing a Transformed Quadratic Function
This is a new technique
This is a previously learned technique
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New: Method 1
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Writing a Transformed Quadratic Function
Lets work this step out
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Practice
(From example 5: )