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The roots of the quadratic function y = 1 / 2 x 2 − 3x + 5 / 2 are the places where the graph intersects the x-axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
The graph of the square function y = x 2 is a parabola. The squaring operation defines a real function called the square function or the squaring function. Its domain is the whole real line, and its image is the set of nonnegative real numbers. The square function preserves the order of positive numbers: larger numbers have larger squares.
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
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Although the chromatic number of the square of a nonplanar graph with maximum degree Δ may be proportional to Δ 2 in the worst case, it is smaller for graphs of high girth, being bounded by O(Δ 2 / log Δ) in this case. [8] Determining the minimum number of colors needed to color the square of a graph is NP-hard, even in the planar case. [9]
The graph of a real single-variable quadratic function is a parabola. If a quadratic function is equated with zero, then the result is a quadratic equation . The solutions of a quadratic equation are the zeros (or roots ) of the corresponding quadratic function, of which there can be two, one, or zero.
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