How is the graph of $$ f(x)=(x-3)^{2}+7 $$ generated from the graph of $$ g(x)=x^{2} $$ ? A. Translate $$ g(x) 3 $$ units right and 7 units downward to generate $$ f(x) $$ B. Translate $$ g(x) 3 $$ units right and 7 units upward to generate $$ f(x) $$ C. Translate $$ g(x) 3 $$ units left and 7 units upward to generate $$ f(x) $$ D. Translate $$ g(x) 3 $$ units left and 7 units downward to generate $$ f(x) $$

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To determine how the graph of $$ f(x) = (x-3)^2 + 7 $$ is generated from the graph of $$ g(x) = x^2 $$, let's analyze the transformations step by step.

1. **Horizontal Translation (Shift Left or Right):**
   - The term $$ (x - 3) $$ inside the squared function indicates a horizontal shift.
   - Specifically, $$ x - 3 $$ means the graph of $$ g(x) $$ is shifted **3 units to the right**.

2. **Vertical Translation (Shift Up or Down):**
   - The "+ 7" outside the squared term indicates a vertical shift.
   - This means the graph is shifted **7 units upward**.

**Summary of Transformations:**
- **Right Shift:** 3 units
- **Upward Shift:** 7 units

**Therefore, the correct transformation is:**
  
**B. Translate $$ g(x) $$ 3 units right and 7 units upward to generate $$ f(x) $$.**

Answer: B
To generate the graph of $$ f(x) = (x-3)^2 + 7 $$ from $$ g(x) = x^2 $$, shift the graph 3 units to the right and 7 units upward. Answer: B

How is the graph of generated from the graph of ?
A. Translate units right and 7 units downward to generate
B. Translate units right and 7 units upward to generate
C. Translate units left and 7 units upward to generate
D. Translate units left and 7 units downward to generate

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How is the graph of generated from the graph of ? A. Translate units right and 7 units downward to generate B. Translate units right and 7 units upward to generate C. Translate units left and 7 units upward to generate D. Translate units left and 7 units downward to generate