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In real analysis, a quadratic function is a real function f such that f(x)=ax2+bx+c for all x in R, where a, b and c are real numbers, with a ≠ 0. (In some situations, a=0 may be permitted.) The graph y=f(x) of such a function is a parabola with its axis parallel to the y-axis, and with its vertex downwards if a>0 and upwards if a<0. The graph cuts the x-axis where ax2+bx+c=0, so the points (if any) are given by the roots (if real) of this quadratic equation. The position of the vertex can be determined by completing the square or by finding the stationary point of the function using differentiation. If the graph cuts the x-axis in two points, the x-coordinate of the vertex is midway between these two points. In this way the graph of the quadratic function can be sketched, and information can be deduced.

Subjects: Mathematics.

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