Students practice graphing translations of parabolas by shifting them vertically and horizontally on coordinate planes.

It looks like you've uploaded a worksheet titled "Translation - Graph" that asks you to draw the translated graph of various functions based on transformations. The task involves understanding how graphs shift vertically and horizontally.

Let’s go through each problem step by step, explain what transformation is happening, and describe how to draw the correct graph.

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🔹 General Rules for Graph Transformations:

- Vertical Shifts:
- $ y = f(x) + k $: Shifts the graph up by $ k $ units.
- $ y = f(x) - k $: Shifts the graph down by $ k $ units.

- Horizontal Shifts:
- $ y = f(x - h) $: Shifts the graph right by $ h $ units.
- $ y = f(x + h) $: Shifts the graph left by $ h $ units.

We’ll assume the original function is a basic parabola (like $ y = x^2 $), since all the graphs shown are quadratic in shape.

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Now let's analyze each question:

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1) 3 units up

- Take the original graph (which appears to be a parabola opening upward with vertex at origin).
- Move every point 3 units upward.
- So, if the original vertex was at $ (0, 0) $, the new vertex is at $ (0, 3) $.
- Draw the same shape, just shifted up.

✔ New Vertex: $ (0, 3) $

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2) 3 units down

- Shift the entire graph down by 3 units.
- Original vertex $ (0, 0) $ → New vertex $ (0, -3) $
- Same shape, just lower.

✔ New Vertex: $ (0, -3) $

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3) 4 units left

- Shift the graph left by 4 units.
- Original vertex $ (0, 0) $ → New vertex $ (-4, 0) $
- The parabola opens upward as before.

✔ New Vertex: $ (-4, 0) $

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4) 4 units right

- Shift the graph right by 4 units.
- Original vertex $ (0, 0) $ → New vertex $ (4, 0) $
- Same shape, moved to the right.

✔ New Vertex: $ (4, 0) $

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5) 4 units down

- Shift down by 4 units.
- Original vertex $ (0, 0) $ → New vertex $ (0, -4) $
- Parabola still opens upward.

✔ New Vertex: $ (0, -4) $

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6) 4 units up

- Shift up by 4 units.
- Original vertex $ (0, 0) $ → New vertex $ (0, 4) $
- Same shape, higher.

✔ New Vertex: $ (0, 4) $

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✔ Summary of Translations:

| Problem | Transformation | New Vertex |
|--------|----------------------|----------------|
| 1 | Up 3 | (0, 3) |
| 2 | Down 3 | (0, -3) |
| 3 | Left 4 | (-4, 0) |
| 4 | Right 4 | (4, 0) |
| 5 | Down 4 | (0, -4) |
| 6 | Up 4 | (0, 4) |

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📌 How to Draw Each Graph:

For each problem:
1. Start with the original parabola $ y = x^2 $ (vertex at origin, U-shaped).
2. Apply the shift:
- For vertical shifts: move the vertex up/down.
- For horizontal shifts: move the vertex left/right.
3. Keep the same shape — just reposition it.

> Example: For #3 (4 units left):
> - Original: vertex at (0,0)
> - New vertex: (-4, 0)
> - Plot points symmetrically around (-4, 0): e.g., (-3,1), (-5,1), (-2,4), (-6,4), etc.

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💡 Tips:

- Always identify the vertex first.
- Use key points (like (1,1), (-1,1), (2,4)) from the original graph and apply the same shift.
- Check the direction: "up/down" affects $ y $, "left/right" affects $ x $.

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If you'd like, I can help generate the actual graphs or sketch them in text form using ASCII art! Let me know.