CHAPTER 9: Quadratic Equations and Functions

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CHAPTER 9Quadratic Equations and Functions

• Lesson 9.3
• Graphing Quadratic Functions

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TERMS

• Quadratic Function can be written in standard
  form y ax2 bx c , where a ? 0
• Parabola graph of a quadratic function (u-shaped)

Parent Function y x2
3

• y ax2 bx c
• If a gt 0 , parabola opens up
• If a lt 0 , parabola opens down (upside down u)

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TERMS

• Vertex lowest (if parabola opens up) or highest
  (if parabola opens down) point

Domain Range
Domain Range
Vertex (3 , 0)
Vertex (0 , 0)
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TERMS

• Axis of symmetry line passing through the vertex
  that divides the parabola into two symmetric
  parts
• Two parts are mirror images of each other

Axis of symmetry x 3
Axis of symmetry x 0
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GRAPH OF A QUADRATIC FUNCTION

• The graph of y ax2 bx c is a parabola
• If a is positive, the parabola opens up
• If a is negative, the parabola opens down
• The vertex has an x-coordinate of
• The axis of symmetry is the vertical line

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GRAPHING A QUADRATIC FUNCTION

• The graph of y ax2 bx c is a parabola
• Find the x-coordinate of the vertex
• Find the y value by plugging x into the equation
• Make a table of values, using x-values to the
  left and right of the vertex
• Plot the points and connect them with a smooth
  curve to form a parabola

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Sketch a graph of y x2 - 2x - 3

• Checklist
• Open up or down?
• Find the vertex
• Make a table of values
• Graph
• Axis of symmetry?

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Sketch a graph of y -2x2 - x 2

• Checklist
• Open up or down?
• Find the vertex
• Make a table of values
• Graph
• Axis of symmetry?

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Sketch a graph of y x2 3x - 4

• Checklist
• Open up or down?
• Find the vertex
• Make a table of values
• Graph
• Axis of symmetry?

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Sketch a graph of y x2 - x 1

• Checklist
• Open up or down?
• Find the vertex
• Make a table of values
• Graph
• Axis of symmetry?

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y x2 x - 2

• Give the coordinates of the vertex
• Write the equation for the axis of symmetry
• Does the function open up or down?

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y -2x2 5x - 4

• Give the coordinates of the vertex
• Write the equation for the axis of symmetry
• Does the function open up or down?

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Using quadratic models in real-life

• A struck baseball follows a path modeled by
• y -0.00993x2 1.1106x 4.1
• where x is the horizontal distance and y is the
  height.
• What is the maximum height of the baseball?

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HOMEWORK

• Page 521
• 22-36 even
• 44-54 even
• 67, 68