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In it, geometrical shapes can be made, as well as expressions from the normal graphing calculator, with extra features. [8] In September 2023, Desmos released a beta for a 3D calculator, which added features on top of the 2D calculator, including cross products, partial derivatives and double-variable parametric equations.
A parabola, a convex curve that is the graph of the convex function () = In geometry , a convex curve is a plane curve that has a supporting line through each of its points. There are many other equivalent definitions of these curves, going back to Archimedes .
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.
If the line is the graph of the linear function () = +, this slope is given by the constant a. The slope measures the constant rate of change of () per unit change in x: whenever the input x is increased by one unit, the output changes by a units: (+) = +, and more generally (+) = + for any number .
Reflective property of a parabola. The reflective property states that if a parabola can reflect light, then light that enters it travelling parallel to the axis of symmetry is reflected toward the focus. This is derived from geometrical optics, based on the assumption that light travels in rays. Consider the parabola y = x 2. Since all ...
The second derivative of a function f can be used to determine the concavity of the graph of f. [2] A function whose second derivative is positive is said to be concave up (also referred to as convex), meaning that the tangent line near the point where it touches the function will lie below the graph of the function.
A cusp in the semicubical parabola = An ordinary cusp is given by =, i.e. the zero-level-set of a type A 2-singularity. Let f (x, y) be a smooth function of x and y and assume, for simplicity, that f (0, 0) = 0. Then a type A 2-singularity of f at (0, 0) can be characterised by:
These are given by the generating family F(t,(x,y)) = t 2 – 2tx + y. The zero level set F ( t 0 ,( x , y )) = 0 gives the equation of the tangent line to the parabola at the point ( t 0 , t 0 2 ). The equation t 2 – 2 tx + y = 0 can always be solved for y as a function of x and so, consider