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The graph provided is a parabola that opens downwards, meaning the coefficient of \( x^2 \) in its equation must be negative. Among the given options:

1. \( y = 10x^2 - 9x + 3 \)
2. \( y = 10x^2 - 9x + 1 \)
3. \( y = -10x^2 - 9x + 1 \)
4. \( y = -10x^2 - 9x + 3 \)

The correct equation must have a negative \( x^2 \) term due to the downward-opening shape, which leaves us with the third and fourth options:
- \( y = -10x^2 - 9x + 1 \)
- \( y = -10x^2 - 9x + 3 \)

Next, the y-intercept of the parabola occurs around \( y = 3 \), which suggests the fourth equation, \( y = -10x^2 - 9x + 3 \), is the best match.

### Answer: \( y = -10x^2 - 9x + 3 \)

Would you like further details or have any questions?

Here are 5 related questions to expand on this concept:
1. How can you determine whether a parabola opens upwards or downwards?
2. How does the value of the constant term in a quadratic equation affect the graph?
3. What role does the coefficient of \( x \) play in shaping the parabola?
4. How can you find the vertex of a parabola given its equation?
5. What are the steps to derive the equation of a parabola from its graph?

**Tip:** When identifying the correct quadratic equation for a graph, always check the sign of the leading coefficient to determine the direction of the parabola.

Which equation best matches the graph shown below?

Learn how to identify the correct quadratic equation for a downward-facing parabola. This question covers concepts like the sign of the quadratic term and the constant's effect on the y-intercept. Best suited for students in Grades 8-10.

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