To answer this question accurately, I'll need more details about the graph you're referring to. If you have the graph available, feel free to upload it, and I will analyze it for you.

However, here's how we typically approach this kind of problem conceptually:

1. Exponential Function (e.g., $f(x) = a^x$): An exponential function grows very rapidly as $x$ increases, depending on its base.

2. Quadratic Function (e.g., $g(x) = ax^2 + bx + c$): A quadratic function typically has a parabolic shape, opening upwards or downwards depending on the sign of the leading coefficient $a$.

To find the interval where the value of the exponential function is greater than the quadratic function, we'd follow these steps:

1. Intersection Points: First, we find where the exponential function and quadratic function intersect. At these points, $f(x) = g(x)$. Solving this equation gives the points of intersection.

2. Compare Function Values: Between these points of intersection, we'd analyze which function is greater. Generally, for small $x$, quadratic functions dominate because exponentials grow slowly at first. However, for larger $x$, the exponential function grows much faster, eventually surpassing the quadratic.

Once you upload the graph or provide more details, I can give you the exact interval.

Do you have the graph to share? Or would you like further details on this process?

---

Here are 5 related questions:

1. How do you find the intersection points of two functions analytically?
2. What are the key characteristics of an exponential function compared to a quadratic function?
3. How does the growth rate of an exponential function compare to a polynomial function in general?
4. What is the behavior of a quadratic function for very large positive and negative values of $x$?
5. How do we determine if one function is greater than another in a given domain?

Tip: When comparing functions, especially exponential and polynomial ones, always pay attention to their behavior at the boundaries of the domain, since exponentials often grow much faster for large $x$.