Question 866555
We start with {{{y=x^2}}}. That is given to us. This is the parent quadratic function/equation. This is the <font color="green">green</font> graph shown below.



We would then "vertically compress by a factor of 1/2". So we would multiply {{{x^2}}} by 1/2 which "squishes" the graph. This is because every point on the graph is now half as high as it used to be (ex: y = 4 ---> y = (1/2)*4 = 2 )



So we now have {{{y = expr(1/2)x^2}}}. This is the <font color="blue">blue</font> graph shown below.



Finally, we "translate down by 2" to get {{{y = expr(1/2)x^2-2}}}. Visually we are just shifting the entire blue graph 2 units down to get the <font color="purple">purple</font> graph.



Below are the graphs of {{{y=x^2}}}, {{{y = expr(1/2)x^2}}}, and {{{y = expr(1/2)x^2-2}}} in <font color="green">green</font>, <font color="blue">blue</font> and <font color="purple">purple</font> respectively.



{{{ drawing(500, 500, -10, 10, -10, 10,



 graph( 500, 500, -10, 10, -10, 10,0,x^2,(1/2)*x^2,(1/2)*x^2-2)



)}}}


The sequence of graphs above (all plotted on the same xy axis) shows us how {{{y=x^2}}} transforms into {{{y = expr(1/2)x^2-2}}}