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The graph of y = x^2 is:
This is shifted horizontally to the left with y = (x + 1)^2
Shifting the graph vertically upwards by 4 units gives the graph of y = x^2 + 2x + 5
y = x^2 is transformed to y = x^2 + 2x + 5 by shifting it horizontally to the left and vertically upwards.
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