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The question asks to identify the equation that represents the curve shown in the graph. This graph appears to be a parabola.

Let's analyze the graph step by step:

### Observing the key points:
- The vertex of the parabola appears to be at \( (2, -3) \).
- The parabola opens upwards, meaning the coefficient of \( x^2 \) is positive.

### Standard form of a parabola:
The general vertex form of a parabola is:

\[
y = a(x - h)^2 + k
\]

Where:
- \( (h, k) \) is the vertex.
- \( a \) determines the direction and width of the parabola.

Since the vertex is at \( (2, -3) \), the equation will have \( h = 2 \) and \( k = -3 \), leading to the equation:

\[
y = (x - 2)^2 - 3
\]

This matches the first option: \( y = (x - 2)^2 - 3 \).

### Final Answer:
The correct equation representing the curve is \( y = (x - 2)^2 - 3 \).

Would you like more details, or do you have any other questions?

Here are 5 related questions to expand your understanding:
1. How do you find the vertex of a parabola from its equation?
2. What role does the value of \( a \) in \( y = a(x - h)^2 + k \) play in determining the parabola's shape?
3. How can you convert a quadratic equation from standard form to vertex form?
4. What is the axis of symmetry for a parabola, and how can you find it?
5. How would the equation change if the parabola opened downwards?

**Tip:** When analyzing a quadratic function, the vertex form is often the most useful for quickly identifying the vertex and the direction of the parabola.

Which equation represents the curve shown on the graph?

Learn how to identify the correct quadratic equation for a parabola from its graph. This example demonstrates how to use the vertex form of a parabola, focusing on recognizing the vertex and orientation of the curve. Suitable for students in Grades 9-10.

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