![]() ![]() The axis of symmetry is x = − 4 2 ( 1 ) = −2. If a 0, a > 0, the parabola opens upward. If a > 0, a > 0, the parabola opens upward. Where a, b, a, b, and c c are real numbers and a ≠ 0. These features are illustrated in Figure 2.į ( x ) = a x 2 + b x + c f ( x ) = a x 2 + b x + c The graph is also symmetric with a vertical line drawn through the vertex, called the axis of symmetry. In either case, the vertex is a turning point on the graph. ![]() If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. One important feature of the graph is that it has an extreme point, called the vertex. The graph of a quadratic function is a U-shaped curve called a parabola. Working with quadratic functions can be less complex than working with higher degree functions, so they provide a good opportunity for a detailed study of function behavior. In this section, we will investigate quadratic functions, which frequently model problems involving area and projectile motion. The cross-section of the antenna is in the shape of a parabola, which can be described by a quadratic function. (credit: Matthew Colvin de Valle, Flickr)Ĭurved antennas, such as the ones shown in Figure 1, are commonly used to focus microwaves and radio waves to transmit television and telephone signals, as well as satellite and spacecraft communication.
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