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.