Quadratic Function

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Quadratic Function

• By Mr. Keung/Ms. Keung

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Abstract

• Currently we are working on quadratic functions
  so we have designed a PowerPoint lesson which has
  been used in our classrooms with success. We
  start with the topic Quadratic Function and
  later extend to the quadratic equations. Our
  students are 8th graders in the John D OBryant
  and 9th graders in the Snowden High, and we both
  use the same textbook, Algebra 1 (Glencoe).
  Essentially we just hook up the Infocus with our
  laptop and conduct the lesson. We both have a
  couple of old computers in our rooms, therefore
  some students can go online together with us
  while we are doing the online exploration part.
  In this particular lesson we are using the gizmo,
  Roots of Quadratic Function, from the
  Explorelearning.com.

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Quadratic Function(y ax2 bx c)

• a, b, and c are called the coefficients.
• The graph will form a parabola.
• Each graph will have either a maximum or minimum
  point.
• There is a line of symmetry which will divide the
  graph into two halves.

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y x2

• a 1, b 0, c 0
• Minimum point (0,0)
• Axis of symmetry x0

yx2
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What happen if we change the value of a and c ?
y3x2
y4x23
y-4x2-2
y-3x2
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Conclusion(y ax2bxc)

• When a is positive,
• When a is negative,
• When c is positive
• When c is negative

• the graph concaves downward.
• the graph concaves upward.
• the graph moves up.
• the graph moves down.

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What happens if b varies?

• Explore
• http//www.explorelearning.com/index.cfm?methodcR
  esource.dspViewResourceID154
• Describe the changes in your own words.

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Solving Quadratic Functions(ax2 bx c 0)

• Since y ax2 bx c , by setting y0 we set up
  a quadratic equation.
• To find the solutions means we need to find the
  x-intercept.
• Since the graph is a parabola, there will be two
  solutions.

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To solve quadratic equations(graphing method)

• X2 - 2x 0
• To solve the equation, put y x2-x into your
  calculator.
• Find the x intercept.
• Two solutions, x0 and x2.

yx2-2x
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Find the Solutions
yx2-4
yx22x-15
y-x25
y-x2-1
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Find the solutions
y-x24x-1
yx22x1
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Observations

• Sometimes there are two solutions.
• Sometimes there is only one solution.
• Sometimes it is hard to locate the solutions.
• Sometimes there is no solution at all.

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Other Methods

• By factoring
• By using the quadratic formula

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The End