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Which quadratic inequality does the graph below represent?

The graph you uploaded shows a parabola that opens upwards, which implies that the quadratic term has a positive coefficient for \( x^2 \). Additionally, the shading is below the curve, indicating that the inequality involves \( \leq \) or \( < \).

Let's analyze the form of the quadratic equation:
1. The parabola opens upwards, so the coefficient of \( x^2 \) must be positive.
2. The vertex of the parabola is at \( (2, -5) \), so the equation should have a vertex form related to that.
3. Since the shading is below the curve, the inequality must be \( y \leq \text{quadratic expression} \).

The general form is \( y \leq 2x^2 - 8x + 3 \).

Thus, the correct inequality is:
\[ y \leq 2x^2 - 8x + 3 \]

### Answer: 
The first option: \( y \leq 2x^2 - 8x + 3 \).

Do you need any further details or explanations? Here are five related questions that might expand on this concept:
1. How do you find the vertex of a quadratic equation in standard form?
2. Why does a positive \( x^2 \) term make the parabola open upwards?
3. How does the inequality symbol affect the graph of a quadratic inequality?
4. Can you convert a quadratic equation to vertex form?
5. How do you determine whether to use \( \leq \) or \( \geq \) for a quadratic inequality?

**Tip**: When graphing quadratic inequalities, always observe the shading (above or below the curve) to determine whether it involves \( \geq \) or \( \leq \).

This lesson explains how to interpret the graph of a quadratic inequality. Explore the solution to the inequality y ≤ 2x^2 - 8x + 3, covering key algebraic concepts such as the vertex, parabola behavior, and shading. Suitable for students in Grades 9-11.

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