To analyze this question, we need to assess the discriminant based on the graph of the quadratic function.

Observations:

• The graph shown is a parabola that opens upward and intersects the x-axis at two distinct points.
• The discriminant ($D = b^2 - 4ac$) determines the nature of the roots of the quadratic equation:
  • $D > 0$: Two distinct real solutions (two x-intercepts).
  • $D = 0$: One real solution (one x-intercept, vertex touches the x-axis).
  • $D < 0$: No real solutions (no x-intercepts, parabola lies completely above or below the x-axis).

Analysis:

Since the parabola intersects the x-axis at two points, the discriminant must be positive ($D > 0$).

Correct Answer:

D. The discriminant is positive, so there are 2 solutions.

Let me know if you'd like further explanation or additional insights! Here are some related questions for practice:

1. How is the discriminant calculated for a given quadratic equation?
2. What does the graph of a parabola look like if the discriminant is negative?
3. How does the sign of the leading coefficient ($a$) affect the shape of a parabola?
4. If the vertex of a parabola touches the x-axis, what can be said about its discriminant?
5. How can the discriminant be used to verify the number of x-intercepts without graphing?

Tip: Always check the number of x-intercepts on a graph to quickly deduce information about the discriminant.