Questions: Assignment 3.2: Transformation of Functions Score: 1 / 9 2 / 9 answered Question 3 Move the sliders h and k so that the graph of y=x^2 gets shifted up units and to the right 2 units. Then type the new function, f(x) in the answer box Don't forget to shift the graph. Using function notation, i.e. f(x)=, enter the function that results from the transformation.

Assignment 3.2: Transformation of Functions Score: 1 / 9 2 / 9 answered Question 3 Move the sliders h and k so that the graph of y=x^2 gets shifted up units and to the right 2 units. Then type the new function, f(x) in the answer box Don't forget to shift the graph. Using function notation, i.e. f(x)=, enter the function that results from the transformation.
Transcript text: Assignment 3.2: Transformation of Functions Score: $1 / 9 \quad 2 / 9$ answered Question 3 Move the sliders $h$ and $k$ so that the graph of $y=x^{2}$ gets shifted up units and to the right 2 units. Then type the new function, $f(x)$ in the answer box Don't forget to shift the graph. Using function notation, i.e. $f(x)=$, enter the function that results from the transformation.
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Solution

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Solution Steps

Step 1: Identify the Original Function

The original function given is \( f(x) = x^2 \).

Step 2: Determine the Transformations

The problem states that the graph of \( y = x^2 \) needs to be shifted up 8 units and to the right 2 units.

Step 3: Apply the Vertical Shift

Shifting the graph up 8 units means adding 8 to the function: \[ f(x) = x^2 + 8 \]

Step 4: Apply the Horizontal Shift

Shifting the graph to the right 2 units means replacing \( x \) with \( (x - 2) \): \[ f(x) = (x - 2)^2 + 8 \]

Final Answer

The transformed function is: \[ f(x) = (x - 2)^2 + 8 \]

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