1. **Problem:** Find the equation of the resulting graph $g(x)$ when $f(x) = x^2 + 2$ is vertically stretched with scale factor 2. 2. **Formula and Explanation:** A vertical stretch by a factor $k$ means multiplying the entire function by $k$. The new function is: $$g(x) = k \cdot f(x)$$ where $k=2$ here. 3. **Apply the formula:** $$g(x) = 2 \cdot (x^2 + 2)$$ 4. **Simplify:** $$g(x) = 2x^2 + 4$$ 5. **Answer:** The equation of the vertically stretched graph is: $$g(x) = 2x^2 + 4$$ This means every $y$-value of the original graph is doubled, stretching it vertically.