5'1 Graphing Quadratic Functions

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5.1 Graphing Quadratic Functions

• Obj introduce and graph quadratic functions as
  parabolas

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Parabola Applications

• Lighting
• Bridges
• Architecture
• Rides (weightless
• state)

La Pedrera - In Barcelona, built by Antoni Gaudí
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Where do you see parabolas?

• NFL large, parabola shaped microphones
• Top of a Volkswagen beetle

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Definitions

• Quadratic Function f(x)ax2 bx c
• Ex. f(x)5x2 3x 2
• Parabola shape of the graph of any quadratic
  function
• Vertex the pt. where the parabola changes
  direction
• Axis of symmetry the imaginary vertical line
  that crosses through the vertex.

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Parts of the graph
Axes of symmetry
vertices
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Identifying Vertex, Axis of Symmetry, y-intercept

• The x-coordinate of the vertex is

The equation of the axis of symmetry is
The y-intercept is wherever x0 f(x)ax2bxc f0)
a(0)2b(0)c f(0)c
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Example

• For the quadratic equation, identify the vertex,
  axis of symmetry, and the y-intercept.

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What determines whether its a smile or a frown?

• If agt0 (a is POSITIVE), its a smile.
• Theres a minimum at vertex.
• If alt0 (a is NEGATIVE), its a frown.
• Theres a maximum at vertex.

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Example

• For the quadratic equation, identify whether it
  has a minimum or maximum, and find the maximum or
  minimum value. Make a table of values that
  includes the vertex.
• Then, state the domain and range.

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Additional Examples
For the quadratic equation a. identify the
vertex, axis of symmetry, and the
y-intercept. b. Make a table of values that
includes the vertex c. Use this to graph the
function. d. Determine whether the function has
a max or a min. e. State the domain and range.