Question 856847
The trickiest part to learn at first is what happens when you add or subtract a value to x.  You already know that the vertex of {{{f(x)=x^2}}} is at (0,0).  If you change to {{{f(x)=(x-3)^2}}}, then you want to know where does the vertex and the rest of the graph go?  Consider x=3.  This makes {{{f(x)=(3-3)^2=0^2=0}}}.  No change has been done to y, only changed was in x.  We moved x three units rightward when we SUBTRACTED 3 from independent variable x.



(Here, h is assumed a positive number): That is a representative example to show that {{{f(x)=(x-h)^2}}}  is the same shape as {{{f(x)=x^2}}} but moved h units to the right.  Pay attention to the operation symbol used.  {{{(x+h)^2}}} is the same as {{{(x-(-h))^2}}} and this would represent, if h itself were a positive number, h units movement to the LEFT. 


The factor, a, shrinks the graph vertically if {{{abs(a)<1}}}, but stretches the graph vertically if {{{abs(a)>1}}}.