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Quadratic Functions

A function of the form

f (x) = ax2 + bx + c

where a, b and c are constants and a ≠  0, is called a quadratic function. For example, the function f (x) = 2x2 = 5x + 1 is quadratic.

However, the function g (x) = 1/x2 is not quadratic.

The graph of quadratic function y = f (x) = ax2 + bx + c is parabola that opens upward or downward according as a > 0 or a < 0. Each parabola has a vertical axis of symmetry and a turning point called a vertex. Typical graphs of parabola are shown in.

It can be shown that the x-coordinate of the vertex of a parabola opening upward or downward is given by –b/2a. The y-coordinate of the vertex is then f ( b/2a ).

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