Graphing Quadratic Functions

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Graphing Quadratic Functions

• Objectives After completing the online lesson,
  student will be able to graph parabolas
  accurately, at least four out of five times.
•                     After completing the online
  lesson, student will be able to identify the
  vertex and axis of symmetry through algebra, at
  least four out of five times.

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• Understand and apply concepts and procedures
  from number sense.
• Understand and apply concepts and procedures
  from geometric sense.
• Understand and apply concepts and procedures
  from algebraic sense.

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Pre-Assessment Quiz

• Before we start todays lesson, lets see what
  you know about graphing parabolas!
• 1) Record your start time.
• 2) Graph the function f(x) 2x²3x-6.
• 3) Clearly label the vertex, line of symmetry,
  and y-intercept.
• 4) Record your stop time.

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Definitions

• A quadratic function is a function of the form
  f(x) ax² bx c, where a ? 0.
• The graph of a quadratic function is always a
  U-shaped curve called a parabola. The
  coefficients a, b, and c help you draw the
  parabola in a coordinate system.

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• y-intercept of the parabola the number c
• line of symmetry of the parabola the vertical
  line whose equation is x -b/2a. This is a
  vertical line that passes through the vertex of
  the parabola.

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U-TryClick on the blank to check the answer.

• 1)Identify the y-intercept and the equation of
  the line of symmetry for the graph of f(x) 3x²
  - 5x 2. 
• In the equation, c ____, so the y-intercept is
  _____.
• In the equation, a ____ and b ____, so the
  equation of the line of symmetry is x _______,
  which reduces to x ________.

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Smiling or Frowning?

• The graph of the quadratic function
• f(x) ax² bx c opens downward (frowning)
• if a is negative, or opens upward (smiling) if a
• is positive.

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U-TryClick on the blank to check the answer. 

• 2)Tell whether the graphs of these quadratic
  functions are smiling or frowning
•  
• f(x) -3x² - 8x 4 ______________       
             
• g(x) 4x² - 4x 7 ______________
• t(n) 5n² - 6n 5 ______________    
             
• S(x) -12x² 3x 13 ______________

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• To sketch the graph of a quadratic function f(x)
  ax² bx c on a coordinate plane
•  
• Step 1 Graph the y-intercept at (0, c)
•  
• Step 2 Graph the vertex at the point where x
  -b/2a and y f(-b/2a)
•  
• Step 3 Draw the line of symmetry through the
  vertex
•  
• Step 4 Sketch a smooth curve from the vertex,
  through the y-intercept
•  
• Step 5 Reflect the line from Step 4 across the
  line of symmetry
•  

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U-TryClick on the function to check the answer. 

• 3 ) Sketch the graphs of these quadratic
  functions on two different coordinate planes
  (clearly label the y-intercept, vertex, and line
  of symmetry)
•  
• f(x) -3x² - 8x 4            and           
  g(x) 4x² - 4x 7

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Post-Assessment Quiz

• Now that the lesson is over, its time to show me
  what youve learned about graphing parabolas
• 1) Record your start time.
• 2) Graph the function f(x) 2x²3x-6.
• 3) Clearly label the vertex, line of symmetry,
  and y-intercept.
• 4) Record your stop time.

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Solution

• a 2 and b 3, so the line of symmetry is x
  -3/4.
• This means that the x-coordinate of the vertex is
  3/4, and the
• y-coordinate is f(-3/4) 2(-3/4)²3(-3/4)-6,
  which equals 57/8
• (or 7.125)
• c -6, so the y-intercept is 6. Reflect this
  point across the line of symmetry, then draw a
  smooth curve.

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