Section 5'1 Graphing Quadratic Functions

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Section 5.1 Graphing Quadratic Functions

• graph quadratic functions
• use quadratic functions to solve real-life
  problems, such as finding comfortable temperatures

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Parabola
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Put these graphs into your calculator
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You should see this
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Now Try These
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You should see this
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• What does the a value in the quadratic form
  affect about the graph?

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Put these into your calculator
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You should see this
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• How does the c value affect the graph?

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Graph of A Quadratic Function

• y ax2 bx c
• a gt 0
• a lt 0
• alt 1
• agt 1
• x-coordinate of the vertex is b
  2a
• axis of symmetry is the vertical line x b
  2a

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Example 1 Graphing a Quadratic Function

• Graph y 2x2 8x 6

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Try the following problems

• Pg. 253-254 20-22

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Example 2 Graphing a Quadratic in Vertex Form

• Graph y - (x 3)2 4

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Try the following problems

• Pg. 253-254 26-28

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Example 3 Graphing a Quadratic in Intercept Form

• Graph y (x 2)(x 4)

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Try the following problems

• Pg. 253-254 32-34

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Example 4 Writing a Quadratic in Standard Form

• Write the quadratic function in standard form
• a) y (x 4)(x 9) b) y 3(x 1)2 8

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Try the following problems

• Pg. 253-254 38, 40, 43

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Example 5 Using a Quadratic in Standard Form

• Researchers conducted an experiment to determine
  temperatures at which people feel comfortable.
  The percent y of test subjects who felt
  comfortable at temperature x (in degrees
  Fahrenheit) can be modeled by
• y -3.678x2 527.3x 18,807

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Example 6 Using a Quadratic in Standard Form

• The Golden Gate Bridge in San Francisco has two
  towers that rise 500 feet above the road and are
  connected by suspension cables as shown. Each
  cable forms a parabola with equation
• y