Here are the essential concepts you must grasp in order to answer the question correctly.
Vertex of a Quadratic Function
The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola. For the function f(x) = (x + 4)^2 - 2, the vertex can be found directly from the vertex form of a quadratic equation, which is f(x) = a(x - h)^2 + k, where (h, k) is the vertex. In this case, the vertex is at (-4, -2).
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Axis of Symmetry
The axis of symmetry for a quadratic function is a vertical line that divides the parabola into two mirror-image halves. It can be determined using the formula x = h, where h is the x-coordinate of the vertex. For the given function, the axis of symmetry is x = -4, indicating that the parabola is symmetric about this line.
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Domain and Range of Quadratic Functions
The domain of a quadratic function is the set of all possible x-values, which is typically all real numbers for parabolas. The range, however, depends on the vertex; if the parabola opens upwards, the range starts from the y-coordinate of the vertex to positive infinity. For f(x) = (x + 4)^2 - 2, the domain is all real numbers, while the range is [-2, ∞) since the vertex is the minimum point.
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Domain & Range of Transformed Functions