Transformation of Quadratic Functions Worksheets - Free Printable

It looks like you've uploaded a worksheet titled "Translation: Graph" that involves translating (shifting) graphs of functions. The task asks you to show the translated graph for each function based on given transformations.

Since I can't view images directly, I’ll help you solve this step-by-step assuming the standard format of such worksheets. Based on your description and typical problems like this, here’s how we can approach it:

---

🔍 General Concept: Translating Graphs

When a graph of a function $ y = f(x) $ is translated:
- Left/Right: Horizontal shift
- $ f(x + h) $ → shifts left by $ h $ units
- $ f(x - h) $ → shifts right by $ h $ units
- Up/Down: Vertical shift
- $ f(x) + k $ → shifts up by $ k $ units
- $ f(x) - k $ → shifts down by $ k $ units

We apply these rules to each problem.

---

Let’s go through each of the six problems one by one. Since the original graph appears to be a parabola, likely $ y = x^2 $ or similar, I'll assume the base graph is a parabola with vertex at the origin unless otherwise stated.

---

📌 Problem 1: 4 units right and 2 units left

Wait — this says “4 units right and 2 units left” → net shift:
$ 4 - 2 = 2 $ units right

So, if the original graph is $ y = f(x) $, then the new graph is:
$ y = f(x - 2) $

✔ Shift the original graph 2 units to the right.

> Example: If original vertex is at (0,0), new vertex is at (2,0)

---

📌 Problem 2: 4 units down and 4 units right

- Right 4 → $ x \to x - 4 $
- Down 4 → $ y \to y - 4 $, so subtract 4 from the output

So, new function: $ y = f(x - 4) - 4 $

✔ Shift original graph 4 units right and 4 units down

> Vertex moves from (0,0) → (4, -4)

---

📌 Problem 3: 3 units left and 4 units left

→ Total: 7 units left

So: $ y = f(x + 7) $

✔ Shift graph 7 units to the left

> Vertex moves from (0,0) → (-7, 0)

---

📌 Problem 4: 4 units right and 5 units right

→ Total: 9 units right

So: $ y = f(x - 9) $

✔ Shift graph 9 units to the right

> Vertex moves from (0,0) → (9, 0)

---

📌 Problem 5: 3 units right and 1 unit down

- Right 3 → $ x \to x - 3 $
- Down 1 → subtract 1 from output

So: $ y = f(x - 3) - 1 $

✔ Shift graph 3 units right and 1 unit down

> Vertex: (0,0) → (3, -1)

---

📌 Problem 6: 4 units left and 1 unit up

- Left 4 → $ x \to x + 4 $
- Up 1 → add 1 to output

So: $ y = f(x + 4) + 1 $

✔ Shift graph 4 units left and 1 unit up

> Vertex: (0,0) → (-4, 1)

---

✔ Summary of Each Transformation

| Problem | Direction | New Graph Rule | Vertex Movement |
|--------|-----------|----------------|------------------|
| 1 | 4 right, 2 left → net 2 right | $ f(x - 2) $ | (0,0) → (2,0) |
| 2 | 4 right, 4 down | $ f(x - 4) - 4 $ | (0,0) → (4,-4) |
| 3 | 3 left + 4 left = 7 left | $ f(x + 7) $ | (0,0) → (-7,0) |
| 4 | 4 right + 5 right = 9 right | $ f(x - 9) $ | (0,0) → (9,0) |
| 5 | 3 right, 1 down | $ f(x - 3) - 1 $ | (0,0) → (3,-1) |
| 6 | 4 left, 1 up | $ f(x + 4) + 1 $ | (0,0) → (-4,1) |

---

🖼️ How to Draw the Translated Graphs

For each problem:
1. Start with the original graph (a parabola opening upward, vertex at origin).
2. Apply the translation as described above.
3. Plot the new vertex and sketch the same shape shifted accordingly.

For example:
- In Problem 2, draw a parabola with vertex at (4, -4), same shape as original.
- In Problem 6, draw a parabola with vertex at (-4, 1).

---

💡 Tips for Accuracy

- Use grid lines carefully.
- Mark the vertex first — it's the easiest point to track.
- Keep the shape the same; only position changes.

---

If you can describe the original graph (e.g., equation or key points), I can give even more precise instructions.

Would you like me to generate a visual description or sketch instructions for any specific problem?