Here are the essential concepts you must grasp in order to answer the question correctly.
Vertex of a Parabola
The vertex of a parabola is the highest or lowest point on its graph, depending on whether it opens upwards or downwards. For the quadratic function given, the vertex can be found from the equation in vertex form, y - k = a(x - h)^2, where (h, k) represents the vertex coordinates. In this case, the vertex is at (3, 1).
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Axis of Symmetry
The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. For a quadratic function in vertex form, the axis of symmetry can be determined using the x-coordinate of the vertex, which is x = h. For the given function, the axis of symmetry is x = 3.
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Domain and Range of Quadratic Functions
The domain of a quadratic function is all real numbers, as there are no restrictions on the input values. The range, however, depends on the direction the parabola opens. If it opens upwards, the range starts from the y-coordinate of the vertex to positive infinity. For the given function, since it opens upwards, the range is [1, ∞).
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Domain & Range of Transformed Functions