Question

Identify the vertex and the axis of symmetry of the graph of the function y = 3(x + 4)2 – 6.(1 point)
Responses

vertex: (4, –6); axis of symmetry: x = 4
vertex: (4, –6); axis of symmetry: x = 4

vertex: (4, 6); axis of symmetry: x = 4
vertex: (4, 6); axis of symmetry: x = 4

vertex: (–4, 6); axis of symmetry: x = –4
vertex: (–4, 6); axis of symmetry: x = –4

vertex: (–4, –6); axis of symmetry: x = –4

Answer 1

To identify the vertex and the axis of symmetry for the function \( y = 3(x + 4)^2 - 6 \), we can use the vertex form of a quadratic equation, which is given by:

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

where \((h, k)\) is the vertex of the parabola, and \(x = h\) is the axis of symmetry.

In your function:
\[ y = 3(x + 4)^2 - 6 \]

We can rewrite it as:
\[ y = 3(x - (-4))^2 - 6 \]

From this, we can identify:
- \(h = -4\)
- \(k = -6\)

Thus, the vertex is at the point \((-4, -6)\).

The axis of symmetry is given by:
\[ x = h = -4 \]

So the answers are:
- Vertex: \((-4, -6)\)
- Axis of symmetry: \(x = -4\)

The correct response from your options is:
**vertex: (–4, –6); axis of symmetry: x = –4**