CPM Homework Banner

For the quadratic function :

  1. Use the idea of completing the square to write it in graphing form.

    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:  

    Generic rectangle left edge


    interior top left

    interior bottom left

    interior bottom right

    bottom edge    +    

    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. Use the graph to explain why the equation has no real solutions.

    Are there any -intercepts?