Solving Equations and Inequalities Graphically

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Solving Equations and Inequalities Graphically
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POLYNOMIALS

• Polynomial Expression
• Polynomial Function
• Polynomial Equation

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Rational Zeros Theorem

• Suppose all the coefficients in the polynomial
  function
• are integers.
• If is a rational zero of f , where c and
• d have no common factors, then
• c is a factor of , and
• d is a factor of the leading coefficient

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Example 1 (part 1)

• Factors of c
• Factors of d

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Example 1 (part 2)

• Look at the graph to see the zeroes must be
  between -2 and -1 or 3 and 4.
• So
  is a factor.
• By division
• Use the Quadratic Formula to find

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How to Solve f(x) 0

• Find the exact solution algebraically (often by
  factoring)
• Draw a complete graph
• Use ZOOM-IN
• Use SOLVE

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Steps for Solving a Problem

• Find an algebraic representation involving
  variables.
• Draw a complete graph of the function
• Find the domain and range
• Determine the values that make sense in the given
  situation
• Draw a graph of the problem situation
• Solve the problem using appropriate methods

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Example

• A fence for a rectangular garden with one side
  against an existing wall is constructed by using
  80 feet of fencing. What is the maximum area
  that can be enclosed?

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Equations with Absolute Values

• Solve this equation algebraically
• The equation says that
• So, solve and

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Inequalities with Absolute Values

• Solve this Inequality Algebraically
• This means
• Solve this inequality