Free Printable Quadratic Transformations Worksheets - Free Printable

Since I can't view or access images directly, I can’t see the specific graphs in your uploaded worksheet. However, I can help you solve the problem if you describe the graphs or provide details about them.

But based on the title and structure of the worksheet — "Identifying Translation - Graph" — this is likely a math exercise where you're given a parent function $ f(x) $ and its transformed version $ g(x) $, and you’re asked to determine the translation (shift) that maps $ f(x) $ to $ g(x) $.

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🔍 General Approach to Identifying Translations

A translation is a shift of a graph without changing its shape. There are two types:

1. Horizontal translation:
- $ g(x) = f(x - h) $:
- If $ h > 0 $: shift right by $ h $ units
- If $ h < 0 $: shift left by $ |h| $ units

2. Vertical translation:
- $ g(x) = f(x) + k $:
- If $ k > 0 $: shift up by $ k $ units
- If $ k < 0 $: shift down by $ |k| $ units

So, for each graph:
- Identify key points on both $ f(x) $ and $ g(x) $
- Compare their positions (e.g., vertex, intercepts, turning points)
- Determine how much the graph has moved horizontally and vertically

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✔ Example Walkthrough (Hypothetical)

Let’s say Problem 1 shows:
- A parabola $ f(x) $ with vertex at $ (0, 0) $
- A translated parabola $ g(x) $ with vertex at $ (2, 3) $

Then:
- The graph shifted 2 units right and 3 units up
- So the translation is: $ (x, y) \to (x + 2, y + 3) $
- Or: $ g(x) = f(x - 2) + 3 $

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📌 How You Can Solve Each Problem

For each numbered graph (1–6), follow these steps:

1. Find a reference point on $ f(x) $, like the vertex or x-intercept.
2. Locate the corresponding point on $ g(x) $.
3. Compare coordinates:
- Horizontal change: $ \Delta x = x_{\text{new}} - x_{\text{old}} $
- Vertical change: $ \Delta y = y_{\text{new}} - y_{\text{old}} $
4. State the translation:
- “Shifted ___ units left/right and ___ units up/down”

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🛠️ Help Me Help You!

Please describe one or more of the graphs in detail. For example:

> "In problem 1, the original function $ f(x) $ is a parabola opening upward with vertex at (0, 0). The translated graph $ g(x) $ has its vertex at (3, -2)."

Or send me a text description of the graphs.

Once I know the positions, I’ll give you the exact translations for all six problems!