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Here is the graph comparing the original function \( f(x) = x^2 + 4 \) (in blue) with the shifted function \( f_2(x) = (x - 7)^2 + 7 \) (in red, dashed line). The new parabola is shifted 7 units to the right and 3 units upwards as requested.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. What effect does shifting a function horizontally and vertically have on its graph?
2. How can you tell the direction of a parabola's opening based on its equation?
3. How do you identify the vertex of a shifted parabola?
4. What happens to a function's graph if you shift it downwards instead of upwards?
5. How can transformations like stretching or compressing a parabola be applied to functions?

**Tip:** When shifting a function horizontally, the transformation affects the variable inside the parentheses, while vertical shifts impact the entire function's output.

Translate the function f(x) = x^2 + 4 by 3 units up and 7 units to the right.

Learn how to translate the quadratic function f(x) = x^2 + 4 by shifting it 3 units up and 7 units to the right. This covers key concepts in function translation and is suitable for high school algebra students.

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