Looking at the graph, we can determine the x-intercepts and y-intercepts.

1. X-intercepts: The x-intercepts are the points where the graph crosses the x-axis (i.e., where $y = 0$). From the graph, the curve crosses the x-axis at $x = -6$ and $x = 4$.

2. Y-intercept: The y-intercept is the point where the graph crosses the y-axis (i.e., where $x = 0$). From the graph, the curve crosses the y-axis at $y = 12$.

Now, let's compare this information with the given answer choices:

• X-intercepts: (-6, 0) and (4, 0)
• Y-intercept: (0, 12)

From this, the correct answer is Option D:

• $x$-intercept: $(-6, 0)$ and $(4, 0)$
• $y$-intercept: $(0, 12)$

Would you like further details or have any questions?

Here are five related questions to expand on this topic:

1. How can you determine the axis of symmetry for a quadratic function?
2. What is the formula to find the vertex of a quadratic function in standard form?
3. How do you calculate the roots of a quadratic equation algebraically?
4. How does the discriminant of a quadratic equation affect the number of x-intercepts?
5. Can a quadratic function have more than two x-intercepts?

Tip: The vertex of a quadratic function $y = ax^2 + bx + c$ is found at $x = -\frac{b}{2a}$, and this x-value gives the axis of symmetry.