SOLUTION: https://answers.yahoo.com/question/index?qid=20200917201613AAEazzn Help with this problem

Question 1165141: https://answers.yahoo.com/question/index?qid=20200917201613AAEazzn
Help with this problem
Found 3 solutions by ikleyn, Boreal, greenestamps:
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.

It is difficult to see and difficult to read.

Answer by Boreal(15235)   (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)

Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

There are two transformations to get from to .

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):

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