Lesson 2'10 Graph y ax2 c

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Lesson 2.10Graph y ax2 c

• GPS
• MM1A1b
• MM1A1c
• MM1A1e

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EQs

• How do we graph the basic functions?
• How do we graph transformations of basic
  functions including vertical shifts, stretches,
  and shrinks, as well as reflections across the x-
  and y-axes?
• How do we relate to a given context the
  characteristics of a function, and use graphs and
  tables to investigate its behavior?

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Vocabulary

• Quadratic function A nonlinear function that
  can be written in the standard form yax2bxc
  where a0.
• Parabola The U-shaped graph of a quadratic
  function.
• Parent quadratic function The most basic
  quadratic function in the family of quadratic
  functions.
• Vertex The lowest or highest point on a
  parabola.
• Axis of symmetry The line that passes through
  the vertex and divides the parabola into two
  symmetric parts.

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Parent Graph y x2
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Example 1Graph y ax2

• Graph y -6x2. Compare the graph with the graph
  of y x2.
• Solution

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Guided Practice for Example 1

• Graph the function. Compare the graph with the
• graph of y x2.

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Example 2Graph y ax2 c

• Graph y 0.5x2 1. Compare the graph with the
  graph of y x2.
• Solution

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Example 3Use a graph
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Guided Practice for Examples2 3

• Graph the function. Compare the graph with the
  graph of yx2.

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• In Example 3, suppose the reflective surface
  extends just 4 meters on either side of the
  origin. Find the domain and range of the
  function in this situation.

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Joke of the Day

• Where do you find a dog with no legs?

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• Right where you left him?