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
Answers
GPT-4o mini
To find the vertex and axis of symmetry of the function \( y = 3(x + 4)^2 - 6 \), we can use the vertex form of a quadratic function, which is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex.
In the given function:
\[ y = 3(x + 4)^2 - 6 \]
We can rewrite it to match the vertex form:
- The expression \( (x + 4) \) can be rewritten as \( (x - (-4)) \), indicating that \( h = -4 \).
- The \( k \) value is \(-6\).
Thus, the vertex is:
\[
(-4, -6)
\]
The axis of symmetry for the parabola is given by the line \( x = h \). Therefore, the axis of symmetry is:
\[
x = -4
\]
So, the correct answer is:
- Vertex: (-4, -6); Axis of symmetry: x = -4
In the given function:
\[ y = 3(x + 4)^2 - 6 \]
We can rewrite it to match the vertex form:
- The expression \( (x + 4) \) can be rewritten as \( (x - (-4)) \), indicating that \( h = -4 \).
- The \( k \) value is \(-6\).
Thus, the vertex is:
\[
(-4, -6)
\]
The axis of symmetry for the parabola is given by the line \( x = h \). Therefore, the axis of symmetry is:
\[
x = -4
\]
So, the correct answer is:
- Vertex: (-4, -6); Axis of symmetry: x = -4