Question: Find the vertex and axis of symmetry of $f(x) = 3(x + 5)^2 + 1$. The vertex is ( , ). The axis of symmetry is x = . Graph: a parabola opening upward, with equation $f(x) = 3(x + 5)^2 + 1$, and the vertex is at $(-5, 1)$; position_hint = center.

1. **State the problem:** Find the vertex and axis of symmetry of the quadratic function $$f(x) = 3(x + 5)^2 + 1$$. 2. **Recall the vertex form of a quadratic function:** $$f(x) = a(x - h)^2 + k$$ where $(h, k)$ is the vertex. 3. **Identify the vertex:** In the given function, $$f(x) = 3(x + 5)^2 + 1$$, rewrite $$x + 5$$ as $$x - (-5)$$. So, $$h = -5$$ and $$k = 1$$. Therefore, the vertex is $$(-5, 1)$$. 4. **Find the axis of symmetry:** The axis of symmetry is the vertical line that passes through the vertex, given by $$x = h$$. So, the axis of symmetry is $$x = -5$$. 5. **Summary:** - Vertex: $$(-5, 1)$$ - Axis of symmetry: $$x = -5$$