Use transformations of $$ f(x)=x^{2} $$ to graph the following function. $$ h(x)=(x+3)^{2}+6 $$ What transformations are needed to graph the function $$ h(x)=(x+3)^{2}+6 $$ ? Choose the correct answer below. A. The graph of $$ f(x)=x^{2} $$ should be horizontally shifted to the left by 3 units and Bertically shifted up by 6 units. The graph of $$ f(x)=x^{2} $$ should be horizontally shifted to the right by 3 units and vertically shifted up by 6 units. C. The graph of $$ f(x)=x^{2} $$ should be horizontally shifted to the right by 3 units and vertically shifted down by 6 units. D. The graph of $$ f(x)=x^{2} $$ should be horizontally shifted to the left by 3 units and vertically shifted down by 6 units.

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UpStudy AI · Accepted Answer

1. Start with the base function:  
   $$
   f(x)=x^2
   $$

2. Replace $$ x $$ with $$ x+3 $$ to obtain:  
   $$
   f(x+3)=(x+3)^2
   $$  
   This transformation shifts the graph horizontally to the left by 3 units.

3. Add 6 to the function to get:  
   $$
   h(x)=(x+3)^2+6
   $$  
   This transformation shifts the graph vertically upward by 6 units.

Thus, the graph of $$ f(x)=x^2 $$ should be horizontally shifted to the left by 3 units and vertically shifted up by 6 units.

The correct answer is A.
The graph of $$ f(x)=x^{2} $$ should be shifted horizontally to the left by 3 units and vertically up by 6 units. The correct answer is A.

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