1. **State the problem:** We are given the function $$h(x) = (-x + 2)^2$$ and the parent function $$f(x) = x^2$$. We need to identify the transformations applied to $$f(x)$$ to get $$h(x)$$. 2. **Rewrite the function:** Notice that $$h(x) = (-x + 2)^2 = (-(x - 2))^2$$. 3. **Recall the parent function:** The parent function is $$f(x) = x^2$$, a parabola with vertex at $$(0,0)$$ opening upwards. 4. **Analyze transformations inside the function:** - The expression $$x - 2$$ inside the square indicates a horizontal shift 2 units to the right. - The negative sign in front of $$x$$ inside the parentheses means a reflection over the y-axis. 5. **Effect of squaring:** Since the entire expression is squared, the negative sign inside does not affect the direction the parabola opens; it still opens upwards. 6. **Vertex location:** The vertex of $$h(x)$$ is at $$(2,0)$$ because the horizontal shift moves the vertex from $$(0,0)$$ to $$(2,0)$$. 7. **Summary of transformations:** - Reflection over the y-axis due to the negative sign inside. - Horizontal shift 2 units to the right. 8. **Note on the user's statement:** The user mentioned reflection over the x-axis and translation up 2 units, but the function $$h(x) = (-x + 2)^2$$ does not translate vertically or reflect over the x-axis. **Final answer:** The function $$h(x) = (-x + 2)^2$$ is obtained by reflecting the parent function $$f(x) = x^2$$ over the y-axis and shifting it 2 units to the right. The vertex is at $$(2,0)$$.