Here are the essential concepts you must grasp in order to answer the question correctly.
Quadratic Functions
A quadratic function is a polynomial function of degree two, typically expressed in the form f(x) = ax^2 + bx + c. The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'. Understanding the general shape and properties of parabolas is essential for sketching their graphs.
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Vertex and Axis of Symmetry
The vertex of a parabola is the highest or lowest point on the graph, depending on its orientation. The axis of symmetry is a vertical line that passes through the vertex, dividing the parabola into two mirror-image halves. For a quadratic function in standard form, the vertex can be found using the formula x = -b/(2a), and the axis of symmetry is given by the equation x = -b/(2a).
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Domain and Range
The domain of a function refers to all possible input values (x-values) for which the function is defined, while the range refers to all possible output values (y-values). For quadratic functions, the domain is typically all real numbers, while the range depends on the vertex: if the parabola opens upwards, the range starts from the y-coordinate of the vertex to positive infinity; if it opens downwards, it extends from negative infinity to the y-coordinate of the vertex.
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