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 $\leq$.