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) = ax² + bx + c, where a, b, and c are constants. The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of 'a'. Understanding the general shape and properties of parabolas is essential for analyzing their equations.
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Vertex of a Parabola
The vertex of a parabola is the highest or lowest point on its graph, depending on whether it opens downwards or upwards. For a quadratic function in vertex form, f(x) = a(x-h)² + k, the vertex is located at the point (h, k). In the given graph, the vertex is at (1/2, 2), which is crucial for writing the function's equation accurately.
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Y-Intercept
The y-intercept of a function is the point where the graph intersects the y-axis, which occurs when x = 0. For quadratic functions, the y-intercept can be found by evaluating the function at x = 0, yielding the value of 'c' in the standard form f(x) = ax² + bx + c. In this case, the y-intercept is at (0, 3), providing a key point for determining the function's equation.
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