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.