Learn about parabolas, their properties, and how to graph them in this introductory lesson on quadratic functions and equations.
Parabolas are a particular type of geometric curve, modelled by quadratic equations. Parabolas are fundamental to satellite dishes and headlights.
In this section we will be graphing parabolas. We introduce the vertex and axis of symmetry for a parabola and give a process for graphing parabolas. We also illustrate how to use completing the square to put the parabola into the form f (x)=a (x-h)^2+k.
The equations of parabolas with vertex (0, 0) are y 2 = 4 p x when the x -axis is the axis of symmetry and x 2 = 4 p y when the y -axis is the axis of symmetry.
Natural circles are common, such as the full moon or a slice of round fruit. The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern machinery possible. In mathematics, the study of the circle has helped inspire the development of geometry, astronomy and calculus.
A circle is a 2-dimensional closed shape that has a curved side whose ends meet to form a round shape. Learn about circles with concepts, properties, and examples.
Essentially, circles around round shapes without any corners or edges. Circles also have to be closed and two-dimensional. If a shape is a three-dimensional circle, it’s actually called a sphere. If a shape looks like a circle but isn’t complete, like a crescent moon, it might be called a “crescent” shape.
This geometry video tutorial provides a basic introduction into circles. It explains how to calculate the area of a circle as well as the circumference of a circle.