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In elementary mathematics a polynomial and its associated polynomial function are rarely distinguished and the terms quadratic function and quadratic polynomial are nearly synonymous and often abbreviated as quadratic. A quadratic polynomial with two real roots (crossings of the x axis). The graph of a real single-variable quadratic function is ...
For linear and quadratic functions, the graph of any function can be obtained from the graph of the parent function by simple translations and stretches parallel to the axes. For example, the graph of y = x 2 − 4 x + 7 can be obtained from the graph of y = x 2 by translating +2 units along the X axis and +3 units along Y axis.
The function f(x) = ax 2 + bx + c is a quadratic function. [16] The graph of any quadratic function has the same general shape, which is called a parabola. The location and size of the parabola, and how it opens, depend on the values of a, b, and c. If a > 0, the parabola has a minimum point and opens upward.
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 ...
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.
Graphs of quadratic functions shifted upward and to the right by 0, 5, 10, and 15. In analytic geometry , the graph of any quadratic function is a parabola in the xy -plane. Given a quadratic polynomial of the form a ( x − h ) 2 + k {\displaystyle a(x-h)^{2}+k} the numbers h and k may be interpreted as the Cartesian coordinates of the vertex ...
In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Power functions – relationships of the form y = a x k {\displaystyle y=ax^{k}} – appear as straight lines in a log–log graph, with the exponent corresponding to ...
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.