To write an inequality that represents the shaded region of the graph, we need to identify the equation of the parabola and then determine the inequality sign based on the shading.

### Step 1: Identify the Equation of the Parabola
Looking at the graph, the parabola seems to open upwards, indicating a standard form of the quadratic function:

\[
y = ax^2 + bx + c
\]

If the vertex is at \((h, k)\) and the equation is in vertex form, it would be:

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

### Step 2: Determine the Inequality
If the shaded region is **above** the parabola, the inequality will be:

\[
y \geq ax^2 + bx + c
\]

If the shaded region is **below** the parabola, the inequality will be:

\[
y \leq ax^2 + bx + c
\]

### Step 3: Interpret the Graph
From the image, since the region is shaded **inside** the parabola, and assuming it opens upwards, the inequality would be:

\[
y \leq ax^2 + bx + c
\]

However, the exact coefficients \(a\), \(b\), and \(c\) would depend on the specific graph and the exact values visible on the axes.

### Conclusion
Without precise coordinates or the equation from the graph, I can state that the inequality is generally of the form:

\[
y \leq ax^2 + bx + c
\]

If you can provide any additional details, such as points on the parabola, I can give you the exact equation.

---

**Would you like further details or have any more questions?**

Here are some questions related to this:

1. How do you derive the equation of a parabola from a graph?
2. What are the steps to convert a quadratic equation from standard form to vertex form?
3. How do you determine if the inequality is strict (using \(>\) or \(<\)) or non-strict (using \(\geq\) or \(\leq\))?
4. How can you find the focus and directrix of a parabola?
5. What are some examples of systems of inequalities involving parabolas?
6. How do you check if a specific point lies within the shaded region?
7. What role does the discriminant play in determining the nature of the graph?
8. How can quadratic inequalities be applied in real-life scenarios?

**Tip:** When writing inequalities for quadratic functions, make sure to check the direction of the parabola and whether the shading is above or below the curve. This will help you choose the correct inequality sign.

Learn how to write an inequality representing the shaded region of a graphed parabola. Understand the standard and vertex forms of quadratic equations and how to interpret the direction of the parabola to determine the correct inequality sign. Suitable for high school students.

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