To determine the number of solutions for the mixed-degree system graphed, we need to find the intersection points between the two curves:

1. Description of the Graph: The graph shows a parabola (a quadratic function) that opens downward and intersects a horizontal line.

2. Intersection Points: Solutions to a system of equations are represented by the points where the graphs intersect. By observing the graph:

   • The parabola intersects the horizontal line in two places.

3. Conclusion: Since there are two points of intersection, there are two solutions to this system.

Answer: The correct choice is two.

Would you like more details, or do you have any further questions?

Here are five related questions you might find helpful:

1. How do we determine the number of solutions for a system with different types of equations (e.g., linear and quadratic)?
2. What happens if a line is tangent to a parabola in a graph?
3. Can a quadratic function and a linear function intersect more than twice?
4. How do we solve systems of equations algebraically when they involve different degrees?
5. What changes about the solutions if the parabola opens upward instead?

Tip: In a mixed-degree system, solutions are found by looking at the points of intersection between the curves. A quadratic and linear equation can intersect at most twice.