On the grid below is shown the parabola y = -2x² and the line y =-2x. (a) Sketch the following graphs on the grid below. i) the graph of a concave down parabola which has the same shape as y=-2x² but has vertex at (-4, 3). Scroll below to the grid. On the menu above the graph, select the parabola icon. Then click on the vertex and another point. Once you click on the grid, you may drag the point to where you would like. You need not click exactly on an integer point on the grid, but try to click as close as possible to the point (-4, 3). ii) the graph of a line parallel to y = -2x that passes through the point (-4, 3). Note: On the menu above the graph, select the line icon. Then click on two points. (b) Report the formula of the parabola in part a.i. You may use vertex form, factored form, or standard form. TIP: Click on the Plot icon (F) next to the answer box to see the graph. y = (c) Report the formula of the line in part a.ii.
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
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