https://file.aiquickdraw.com/mathbot/file/1728316379858ggn01y3v.jpg

The graph shown is a parabola that touches the x-axis at exactly one point, which suggests that it has one real root. This happens when the discriminant of a quadratic equation is equal to zero.

### Discriminant Formula:
For a quadratic equation of the form \( ax^2 + bx + c = 0 \), the discriminant (\( \Delta \)) is given by:
\[
\Delta = b^2 - 4ac
\]

- If \( \Delta > 0 \), the quadratic equation has two distinct real roots.
- If \( \Delta = 0 \), the quadratic equation has exactly one real root (the graph touches the x-axis once).
- If \( \Delta < 0 \), the quadratic equation has no real roots (the graph does not touch the x-axis).

Since the graph touches the x-axis at one point, the discriminant must be 0. Therefore, the correct value for the discriminant is **0**.

Would you like any further explanation or details?

Here are some related questions to deepen your understanding:
1. How do the roots of a quadratic equation relate to its discriminant?
2. What happens to the discriminant if the graph has two distinct x-intercepts?
3. How does the graph change if the discriminant is negative?
4. Can the graph ever have a negative discriminant if it touches the x-axis?
5. What does the vertex of the parabola represent in this scenario?

**Tip**: The discriminant is a powerful tool to quickly assess how many real solutions a quadratic equation has just by looking at the graph.

Based on the graph, what could be the value of the discriminant?

Understand how to determine the discriminant of a quadratic equation based on the graph of a parabola. The graph in this example touches the x-axis at one point, indicating that the discriminant is zero. Learn the relationship between the discriminant and the number of real roots.

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