Identify the vertex, axis of symmetry, maximum or minimum, and domain and range of each function.
7. f(x) = 2(x+9)^2 - 4
The given function is in the form f(x) = a(x-h)^2 + k, where (h, k) is the vertex.
Comparing with the given function f(x) = 2(x+9)^2 - 4, we can see that the vertex form of the function is f(x) = 2(x-(-9))^2 - 4.
From this comparison, we can identify the following information:
- The vertex is (-9, -4). This means the graph of the function is symmetric about the vertical line x = -9.
- The coefficient "a" in the function, which is 2, is positive. This indicates that the parabola opens upward, so the vertex represents the minimum point on the graph.
- The domain of the function is all real numbers since there are no restrictions on the values of x.
- The range of the function is y ≥ -4, which means the function has a minimum value of -4, but can take on any value larger than -4.
Summary:
- Vertex: (-9, -4)
- Axis of Symmetry: x = -9
- Minimum value: -4
- Domain: all real numbers (-∞, ∞)
- Range: all real numbers greater than or equal to -4 (y ≥ -4)