Solving Quadratic Equation by Graphing

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Solving Quadratic Equation by Graphing

• Section 6.1

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Quadratic Equation

• y ax2 bx c
• ax2 is the quadratic term.
• bx is the linear term.
• c is the constant term.
• The highest exponent is two therefore, the
  degree is two.

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Identifying Terms

• Example f(x)5x2-7x1
• Quadratic term 5x2
• Linear term -7x
• Constant term 1

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Identifying Terms

• Example f(x) 4x2 - 3
• Quadratic term 4x2
• Linear term 0
• Constant term -3

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Identifying Terms

• Now you try this problem.
• f(x) 5x2 - 2x 3
• quadratic term
• linear term
• constant term

5x2 -2x 3
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Quadratic Solutions

• The number of real solutions is at most two.

No solutions
One solution
Two solutions
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Solving Equations

• When we talk about solving these equations, we
  want to find the value of x when y 0. These
  values, where the graph crosses the x-axis, are
  called the x-intercepts.
• These values are also referred to as solutions,
  zeros, or roots.

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Identifying Solutions

• Example f(x) x2 - 4

Solutions are -2 and 2.
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Identifying Solutions

• Now you try this problem.
• f(x) 2x - x2
• Solutions are 0 and 2.

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Graphing Quadratic Equations

• The graph of a quadratic equation is a parabola.
• The roots or zeros are the x-intercepts.
• The vertex is the maximum or minimum point.
• All parabolas have an axis of symmetry.

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Graphing Quadratic Equations

• One method of graphing uses a table with
  arbitrary
• x-values.
• Graph y x2 - 4x
• Roots 0 and 4 , Vertex (2, -4) ,
• Axis of Symmetry x 2

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Graphing Quadratic Equations

• Try this problem y x2 - 2x - 8.
• Roots
• Vertex
• Axis of Symmetry

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Graphing Quadratic Equations

• The graphing calculator is also a helpful tool
  for graphing quadratic equations.
• Refer to classwork1 for directions for graphing
  quadratic equations on the Casio.