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how can the equation (x+2)^2+1 be obtained by applying a horizontial translation to the graph of y=(x-2)^2+1


By obseving that your equation y=(x+2)^2+1 is the same as y=((x+4)-2)^2+1 = y=(x+(4+ (-2))^2+1. Since you're ading to the x value, this is a shift to the left.

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