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For the quadratic function :

  1. Complete the square to write the equation in graphing form.

    Use the Math Notes box.

    Example 3: Solve  by completing the square.

    Solution: This method works most efficiently when the coefficient of  is .
    Rewrite the equation as . Rewrite the left side as an incomplete square.

    Complete the square and rewrite as

    Take the square root of both sides, . Solving for  reveals that  or .

  2. State the vertex and sketch a graph of the parabola.

    In the standard equation, the vertex is .

  3. What does the graph tell you about the solutions to the equation ? Explain.

    Are there any -intercepts?