https://file.aiquickdraw.com/mathbot/file/1726459231810wg7cdnrw.jpg

Let's go through each part of the question based on the graph provided:

(a) **Find the domain of \( f \):**
   - The graph shows that the function \( f(x) \) exists for all values of \( x \) from \( x = -2 \) to \( x = 12 \). 
   - Therefore, the domain of \( f \) is \( [-2, 12] \).

(b) **Find the range of \( f \):**
   - The minimum value of \( f(x) \) on the graph is at \( y = -4 \) and the maximum value is at \( y = 9 \).
   - Therefore, the range of \( f \) is \( [-4, 9] \).

(c) **Find \( f(-2) \):**
   - From the graph, at \( x = -2 \), the function \( f(x) \) is at \( y = 9 \).
   - So, \( f(-2) = 9 \).

(d) **Find the values of \( x \) for which \( f(x) = -6 \):**
   - Looking at the graph, \( f(x) \) never reaches \( -6 \). The lowest point of the graph is \( y = -4 \).
   - Therefore, there are no values of \( x \) for which \( f(x) = -6 \).

(e) **Find the points where the graph of \( f \) crosses the \( x \)-axis:**
   - The graph crosses the \( x \)-axis at \( x = 2 \) and \( x = 8 \).
   - Therefore, the points are \( (2, 0) \) and \( (8, 0) \).

Would you like further details or have any questions?

Here are some related questions for deeper understanding:

1. What is the vertex form of a parabola, and can it be determined from this graph?
2. How do you find the axis of symmetry of a parabolic function like this one?
3. What are the steps to determine the domain and range of more complex functions?
4. How can we algebraically verify the points where a function crosses the \( x \)-axis?
5. What happens to the domain and range if this graph was shifted vertically or horizontally?

**Tip:** When analyzing a graph, always note the critical points such as intercepts, maximums, minimums, and endpoints to understand the function's behavior fully.

Find the domain and range of the quadratic function, values of f(x) at specific points, and where the function crosses the x-axis based on the given graph.

Explore how to find the domain, range, and intercepts of a quadratic function from a graph. Understand how to evaluate function values at given points and solve for when f(x) equals specific values. Suitable for Grades 8-10.

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