https://file.aiquickdraw.com/mathbot/file/1728758792630btfzrgf8.jpg

To solve this question, let's analyze the given graph and the claims one by one.

The blue graph is a **parabola**, and the orange graph is a **line**. We are asked which two of the following claims are true.

### Claims:

1. **The line has a root at \( x = 5, 1 \):**
   - A root is where a graph intersects the x-axis (i.e., where \( y = 0 \)).
   - The line in the graph does not intersect the x-axis at \( x = 5 \). Instead, it intersects the x-axis closer to \( x = 4.5 \).
   - Therefore, **this claim is false**.

2. **The line and the parabola intersect at \( x = 3, 1 \):**
   - The point \( (3, 1) \) seems to be where the line and the parabola intersect based on the graph.
   - Therefore, **this claim is true**.

3. **The parabola has a root at \( x = -3, 0 \):**
   - A root of the parabola is where it intersects the x-axis, which is at \( x = -3 \).
   - Therefore, **this claim is true**.

4. **The parabola has a root at \( x = -0.5 \):**
   - The parabola has another root around \( x = 1 \), but not at \( x = -0.5 \).
   - Therefore, **this claim is false**.

### Conclusion:

The correct answers are:
- **The line and the parabola intersect at \( x = 3, 1 \).**
- **The parabola has a root at \( x = -3, 0 \).**

Would you like more details or explanations? Here are five related questions:

1. What are the standard equations for a parabola and a line?
2. How do you find the roots of a parabola algebraically?
3. What is the geometric significance of an intersection point between two graphs?
4. How can you verify the intersection point of two curves using algebra?
5. What is the vertex form of a quadratic equation?

**Tip:** To find where two graphs intersect, set their equations equal to each other and solve for the \( x \)-coordinates of the intersection points.

Which two of the claims hold? The blue graph is called a parabola.

Determine the correct claims about the intersection of a line and a parabola. Explore key concepts in quadratic equations and graph analysis, including identifying roots and intersections. Suitable for students in Grades 9-10.

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