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Let's break down and solve the questions based on the provided graph of the quadratic equation \( y = x^2 - x - 2 \).

1. **How many roots does the equation \( x^2 - x - 2 = 0 \) have?**
   - From the graph, we can see that the parabola intersects the x-axis at two points, so **there are 2 roots**.

2. **What are these roots?**
   - The roots are the x-values where the parabola intersects the x-axis. From the graph, it intersects the x-axis at \( x = -1 \) and \( x = 2 \).
   - So, the roots are \( x = -1 \) and \( x = 2 \).

3. **What are the coordinates of the y-intercept?**
   - The y-intercept occurs where \( x = 0 \). Substituting \( x = 0 \) into the equation \( y = x^2 - x - 2 \), we get:
   \[
   y = 0^2 - 0 - 2 = -2
   \]
   - So, the y-intercept is \( (0, -2) \).

4. **What are the coordinates of the turning point?**
   - The turning point is the vertex of the parabola. From the graph, the vertex appears to be at \( x = \frac{1}{2} \), and at \( y = -\frac{9}{4} \).
   - So, the turning point coordinates are approximately \( \left( \frac{1}{2}, -\frac{9}{4} \right) \).

5. **Is the turning point a maximum or a minimum?**
   - The parabola opens upwards, indicating that the turning point is a **minimum**.

### Answers Summary:
1. **Number of roots**: 2 roots.
2. **Roots**: \( x = -1 \) and \( x = 2 \).
3. **y-intercept**: \( (0, -2) \).
4. **Turning point**: \( \left( \frac{1}{2}, -\frac{9}{4} \right) \).
5. **Turning point is a**: minimum.

Would you like any further explanation on any part? 

Here are 5 related questions to consider:
1. How do you find the vertex of a quadratic equation using the formula?
2. What is the axis of symmetry of the quadratic equation given?
3. How can you derive the quadratic formula from completing the square?
4. What does the discriminant tell us about the roots of a quadratic?
5. How do you factor \( x^2 - x - 2 \) algebraically?

**Tip:** The turning point (vertex) of a quadratic \( y = ax^2 + bx + c \) can be found using the formula \( x = -\frac{b}{2a} \).

Please solve correctly: y = x^2 - x - 2, find the roots, y-intercept, turning point, and determine if it is a maximum or minimum.

This tutorial solves the quadratic equation y = x^2 - x - 2 by identifying the roots, y-intercept, and turning point from the graph. It also determines whether the turning point is a maximum or minimum. Suitable for students in Grades 9-10 learning about quadratic equations.

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