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 Intercepts
The vertex of a parabola is the highest or lowest point on the graph, depending on its orientation. The intercepts are the points where the graph crosses the axes, specifically the x-intercepts (roots) and the y-intercept. Identifying these points is crucial for accurately sketching the graph of the quadratic function and understanding its behavior.
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Axis of Symmetry
The axis of symmetry of a parabola is a vertical line that divides the graph into two mirror-image halves. For a quadratic function in standard form, the axis of symmetry can be found using the formula x = -b/(2a). This concept is important for graphing the parabola and helps in determining the vertex and the overall shape of the graph.
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