Question 1165141
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There are two transformations to get from {{{y=x^2}}} to {{{y=(x+2)^2-3}}}.<br>
To determine the order of the transformations, consider how you would evaluate the new function for a given x value: add 2, square it, then subtract 3.<br>
So the adding 2 is the first transformation, and the subtracting 3 is the second.<br>
The graph of {{{y=x^2}}} has it minimum value when x=0; that value is 0.  So the vertex of the graph is at (0,0).<br>
{{{graph(400,400,-4,4,-4,20,x^2)}}}<br>
The first transformation is from {{{y=x^2}}} to {{{y=(x+2)^2}}}.  That transformation moves the whole graph 2 units to the LEFT.<br>
Moving the graph LEFT when the transformed equation is x PLUS 2 squared is confusing to many beginning students.  But it makes perfect sense if you look at it this way:<br>
The graph of {{{y = (x+2)^2}}} has its minimum value when x+2=0 -- but that is when x = -2.<br>
So now the vertex is at (-2,0).<br>
So the first transformation moves the whole graph 2 units to the left:<br>
{{{graph(400,400,-4,4,-4,20,x^2,(x+2)^2)}}}<br>
The second transformation is from {{{y=(x+2)^2}}} to {{{(x+2)^2-3}}}.  It should be easy to understand that this transformation simply moves the whole graph down 3 units; so now the vertex is at (-2,-3):<br>
{{{graph(400,400,-4,4,-4,20,x^2,(x+2)^2,(x+2)^2-3)}}}<br>