Question 1165141: https://answers.yahoo.com/question/index?qid=20200917201613AAEazzn
Help with this problem Found 3 solutions by ikleyn, Boreal, greenestamps:Answer by ikleyn(52777) (Show Source):
You can put this solution on YOUR website! g(x)=(x+2)^2-3
transform the y=x^2 parabola
2 places to the left (opposite the sign +2)
and 3 places downward (the -3)
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.
So the adding 2 is the first transformation, and the subtracting 3 is the second.
The graph of has it minimum value when x=0; that value is 0. So the vertex of the graph is at (0,0).
The first transformation is from to . That transformation moves the whole graph 2 units to the LEFT.
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:
The graph of has its minimum value when x+2=0 -- but that is when x = -2.
So now the vertex is at (-2,0).
So the first transformation moves the whole graph 2 units to the left:
The second transformation is from to . 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):
