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) = 4 - (x - 1)², the vertex can be found by identifying the values of x and y at which the function reaches its maximum or minimum. In this case, the vertex is at the point (1, 4).
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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 the form f(x) = a(x - h)² + k, the axis of symmetry is given by the line x = h. In the function f(x) = 4 - (x - 1)², the axis of symmetry is x = 1.
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Domain and Range of Quadratic Functions
The domain of a quadratic function is the set of all possible input values (x-values), which is typically all real numbers for parabolas. The range is the set of possible output values (y-values), which depends on the vertex. For f(x) = 4 - (x - 1)², the range is y ≤ 4, as the vertex represents the maximum point of the parabola.
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Domain & Range of Transformed Functions