Observe the graph:
\The parent function is quadratic function
.
The graph is reflected in the
-axis.
Minimum point of the parent function is
.
Maximum point of
is
.
The parent graph is translated by
units down.
The graph of
appears to be
reflected in the
-axis ,
units to the left and translated
units down.
Let
represents the dilation.
So far, we have
.
Use the point
to determine the dilation.





Since
, the graph compressed vertically.
The function is
.
Therefore, the graph of
is the graph of
translated
units to the left, compressed vertically, reflected in the
-axis, and translated
units down.
Parent function is
.
The graph of
is the graph of
translated
units to the left, compressed vertically, reflected in the
-axis, and translated
units down.