To solve this problem, let's analyze the graph.

The graph shows a parabola opening upwards, with its vertex at the point $(2, -3)$. From this, we can derive the general form of the quadratic function:

$y = a(x - h)^2 + k$ where $(h, k)$ is the vertex. For this parabola, the vertex is $(2, -3)$, so the equation becomes:

$y = a(x - 2)^2 - 3$

Now, we need to determine the value of $a$. The graph passes through the point $(0, 1)$, so we can substitute $x = 0$ and $y = 1$ to find $a$:

$1 = a(0 - 2)^2 - 3$ $1 = a(4) - 3$ $1 + 3 = 4a$ $4 = 4a \quad \Rightarrow \quad a = 1$

Thus, the quadratic equation representing the parabola is:

$y = (x - 2)^2 - 3$

Since the graph shows the area below the parabola shaded, we are dealing with a quadratic inequality where the values of $y$ are less than or equal to the equation of the parabola. Therefore, the inequality is:

$y \leq (x - 2)^2 - 3$

This is the quadratic inequality represented by the graph.

Would you like further clarification or details on this? Here are some related questions to expand on this concept:

1. What are the different forms of a quadratic function, and how can they be used in inequalities?
2. How do you determine whether to use $\leq$ or $\geq$ in quadratic inequalities based on the graph?
3. How can you find the vertex of a parabola given its quadratic equation?
4. How does the value of $a$ affect the shape of a parabola?
5. How can you determine the axis of symmetry for a quadratic graph?

Tip: When analyzing quadratic graphs, always check the direction in which the parabola opens (upwards or downwards) to determine the appropriate inequality.