https://r2.erweima.ai/mathbot/image/1725758329531b8afiuqg.jpg

The question involves a quadratic function graph and asks for the positions (roots) of the object on the x-axis.

The image presents a parabola that opens downwards, and it's symmetric with respect to the vertical axis.

To solve the problem of determining the x-intercepts (where the parabola crosses the x-axis):

1. **Locate the x-intercepts**: These are the points where the graph crosses the x-axis (y = 0). From the image, we can estimate the positions on the x-axis.

Looking closely:
- One root is approximately at \(x = -2\).
- The other root is at \(x = 2\).

Thus, the roots or x-intercepts of the quadratic function are approximately \(-2\) and \(2\), which correspond to the real solutions of the equation derived from the graph.

The third box in the image seems to be asking for the axis of symmetry. This is the line that goes through the vertex of the parabola. Since the parabola is symmetric around the vertical axis, the axis of symmetry is at \(x = 0\).

So, the answers for this question should be:
- \(x_1 = -2\)
- \(x_2 = 2\)
- \(x_3 = 0\) (axis of symmetry).

Would you like any further details or clarifications on this? Here are five related questions to deepen understanding:

1. How can we algebraically find the roots of a quadratic function?
2. What is the importance of the axis of symmetry in a quadratic function?
3. How can the vertex of a parabola be determined from the equation of the quadratic function?
4. What is the general form of a quadratic function?
5. How does the direction in which a parabola opens relate to its leading coefficient?

**Tip:** When solving quadratic functions graphically, always look for the x-intercepts, vertex, and axis of symmetry to gain full understanding of the graph's behavior.

Learn how to find the x-intercepts and axis of symmetry of a quadratic function using a graphical method. This problem involves a downward-opening parabola with roots at approximately x = -2 and x = 2, and the axis of symmetry at x = 0. Suitable for Grades 8-10.

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