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In mathematics, a quadratic function of a single variable is a function of the form [1] = + +,,where is its variable, and , , and are coefficients.The expression + + , especially when treated as an object in itself rather than as a function, is a quadratic polynomial, a polynomial of degree two.
A freshwater aquatic food web. The blue arrows show a complete food chain (algae → daphnia → gizzard shad → largemouth bass → great blue heron). A food web is the natural interconnection of food chains and a graphical representation of what-eats-what in an ecological community.
Food chain in a Swedish lake. Osprey feed on northern pike, which in turn feed on perch which eat bleak which eat crustaceans.. A food chain is a linear network of links in a food web, often starting with an autotroph (such as grass or algae), also called a producer, and typically ending at an apex predator (such as grizzly bears or killer whales), detritivore (such as earthworms and woodlice ...
Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
In real-world ecosystems, there is more than one food chain for most organisms, since most organisms eat more than one kind of food or are eaten by more than one type of predator. A diagram that sets out the intricate network of intersecting and overlapping food chains for an ecosystem is called its food web . [ 6 ]
Graph of a linear function Graph of a polynomial function, here a quadratic function. Graph of two trigonometric functions: sine and cosine. A real function is a real-valued function of a real variable, that is, a function whose codomain is the field of real numbers and whose domain is a set of real numbers that contains an interval.
While a parabolic arch may resemble a catenary arch, a parabola is a quadratic function while a catenary is the hyperbolic cosine, cosh(x), a sum of two exponential functions. One parabola is f(x) = x 2 + 3x − 1, and hyperbolic cosine is cosh(x) = e x + e −x / 2 . The curves are unrelated.
In the theory of quadratic forms, the parabola is the graph of the quadratic form x 2 (or other scalings), while the elliptic paraboloid is the graph of the positive-definite quadratic form x 2 + y 2 (or scalings), and the hyperbolic paraboloid is the graph of the indefinite quadratic form x 2 − y 2. Generalizations to more variables yield ...