For the quadratic function
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
Complete the square and rewrite as
Take the square root of both sides,
. Solving for reveals that or .
State the vertex and sketch a graph of the parabola.
In the standard equation, the vertex is (
Use the graph to explain why the equation
has no real solutions.
Are there any