The graph represents the quadratic function $y = x^2 - 2x - 3$, and the task is to find the coordinates of points A, B, C, and D, which are labeled on the graph.

Let's identify each point based on the graph:

1. Point A is on the graph where it intersects the $y$-axis, which is the $y$-intercept. From the graph, this point is clearly located at $(-1, 0)$.

2. Point B lies below the x-axis where the curve is at a negative value. From the graph, this point is approximately at $(0, -3)$.

3. Point C is the lowest point of the parabola, known as the vertex. According to the graph, the vertex appears to be at $(1, -4)$.

4. Point D is where the graph crosses the $x$-axis on the right side. From the graph, this point is at $(3, 0)$.

Coordinates of the points:

• $A (-1, 0)$
• $B (0, -3)$
• $C (1, -4)$
• $D (3, 0)$

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

1. How do you determine the x-intercepts of a quadratic function algebraically?
2. What is the formula for finding the vertex of a parabola?
3. How does the discriminant of a quadratic function relate to its graph?
4. Can you factor the quadratic function $y = x^2 - 2x - 3$ to find the x-intercepts?
5. What is the significance of the symmetry in the graph of a quadratic function?

Tip: The vertex form of a quadratic function can be helpful when graphing parabolas or finding the minimum or maximum points.