Sketching Graphs of y Squared

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Given a graph ofwe can sketch the graphequivalent to by making the following observations.

  1. cannot be negative since we cannot take the square root of a negative number to obtain a real number. Ifis negative for any value ofthese values ofdo not appear in the domain ofand these points cannot be plotted. Any parts of the graph for whichmust be discarded.

  2. When we take the square root, ifthen we have two y values, equal in magnitude and opposite in sign. We plot the pointsandThe– axis becomes a line of symmetry.

  3. Any rootsremain roots of

  4. Values ofless than 1 will be increased after square rooting and values ofgreater than 1 will be decreased.

Example: Sketch the graph of

The graph ofis shown below.

The graph ofis shown below.

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