# Given f(x) = -(x+2)^2 - 5, explain how the graph of the function changes at each transformation and give the coordinates of 3 points per phase of the graph.

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You need to start with the identity f(x) = y, hence, substituting x + 2 for x, the graph f(x+2) = y is obtained by translating the graph f(x)=y to the left by 2 units.

Notice that f(x+2) is multiplied by -1, hence the graph of y = -f(x+2) is obtained by reflecting the graph of y=f(x+2) throuh the x axis.

Notice also that the graph of y = -f(x+2) - 5 is obtained by translating the graph of y=-f(x+2) down by 5 units.

Sketching the new graph obtained after a series of transformation were performed yields:

-(x+2)^{2}-5

a= -1; h= -2; k= -5

(-) = reflects the graph on/ in the x-axis

1= since a<0, the graph opens down.

h & k translates the graph by the given units. That is it stretches the graph vertically or horizontally.

Therefore, h (-2) translates the graph by a factor of 2, and

K (-5) translates the graph 5 units down.