https://file.aiquickdraw.com/mathbot/file/1726202649005kc93ewmt.jpg

We are given the function:

\[
f(x) = 3(x - 4)^2 + 7
\]

We are asked to determine whether the axis of symmetry is \(x = -7\).

### Step 1: Identify the form of the function

This function is in the **vertex form** of a quadratic equation, which is given by:

\[
f(x) = a(x - h)^2 + k
\]

Where:
- \(h\) represents the x-coordinate of the vertex.
- \(k\) represents the y-coordinate of the vertex.
- The axis of symmetry is the vertical line \(x = h\).

### Step 2: Determine the axis of symmetry

From the given equation \(f(x) = 3(x - 4)^2 + 7\):
- The value of \(h = 4\).

Therefore, the axis of symmetry is **\(x = 4\)**, not \(x = -7\).

### Conclusion:

The statement that the axis of symmetry is \(x = -7\) is **false**.

---

Do you have any questions or would you like more details? 

Here are some related questions you might find useful:
1. How do you determine the vertex of a parabola from its equation?
2. Why does the value of \(h\) determine the axis of symmetry in the vertex form?
3. What is the geometric significance of the axis of symmetry in a parabola?
4. How does changing the coefficient \(a\) affect the graph of a quadratic function?
5. Can the axis of symmetry ever be a non-vertical line for a quadratic function?

**Tip:** The axis of symmetry of a parabola is always vertical and goes through the vertex.

Determine whether the statement is true or false. The axis of symmetry of the function f(x) = 3(x - 4)^2 + 7 is x = -7.

Learn how to determine the axis of symmetry for the quadratic function f(x) = 3(x - 4)^2 + 7. This problem covers the vertex form of quadratic equations and how to find the axis of symmetry. Suitable for students in Grades 9-10.

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