Examine the graph at right that shows three parabolas. The graph of $f(x) = x^2$ is shown as a dashed curve.

1. What is the domain of $f(x)$? The range?

2. Write possible equations for the two other parabolas.

   Hint (b):

   Notice the location of each vertex.

   More Help (b):

   Notice that one is vertically stretched and the other is inverted and vertically compressed.

   Answer (b):

   $g(x)\approx2(x-6)^2+3\\\\h(x)\approx -\frac{1}{2}(\textit{x}-6)^2+3$

3. What is the domain of $g(x)$? The range?

   Answer (c):

   Domain = all real numbers
   Range $= y ≥ 3$