Definition parabolic relationship

Parabolic | Definition of Parabolic by Merriam-Webster

definition parabolic relationship

Parabola. A u-shaped curve with certain specific properties. Formally, a parabola is defined as follows: For a given point, called the focus, and a given line not. In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately . A parabola can be defined geometrically as a set of points ( locus of points) in the Euclidean plane: A parabola is a set of points, such that for any. a determines the width and the direction of the parabola: The larger |a| becomes, the So in looking at the relationship of the vertices based on these changing In this case, our c-value is our maximum point, meaning there's only one point.

Even if we have an equation like this where b and c both equal zero, it's still considered quadratic.

PARABOLA - formula and definitions of parabola - Latus rectum of a parabola

If that happens, we get the simplest form of a quadratic relationship: This works because it turns out that it's the x squared component that's absolutely necessary for a relationship to be quadratic.

So, unlike b and c, a must never equal zero because that will remove the x squared from the formula since zero multiplied by anything is zero. One of the first places you'll encounter a quadratic relation in physics is with projectile motion. This makes sense if you think about how a projectile travels through the air over time.

parabolic - Dictionary Definition :

Imagine you're tossing a baseball straight up in the air. Let's try visualizing this with a height vs. Over time the ball goes up to a maximum height, and then back down to the starting height again when you catch it.

A parabola is a good indication of a quadratic relationship We can see our graph creates an upside-down parabola, which is the sort of thing you might expect from a quadratic relation.

To make absolutely sure the relation between height and time is quadratic, we'll also look at the vertical equation for projectile motion that deals with position and time: Let's first recall what each variable does to the shape and position of the parabola The larger a becomes, the wider the parabola.

Parabola - Wikipedia

If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward. So in looking at the relationship of the vertices based on these changing variables, which one will have the most interesting impact?

definition parabolic relationship

Will every variable create a relationship amongst the vertices? Let's investigate a's effect first. In our example here, the vertex is always at 0,0.

Let's look at c next since it's naturally the next easiest to understand. Last, let's look at the effect of b on the relationship of the vertices. Parabolas can open up, down, left, right, or in some other arbitrary direction.

definition parabolic relationship

Any parabola can be repositioned and rescaled to fit exactly on any other parabola—that is, all parabolas are geometrically similar. Parabolas have the property that, if they are made of material that reflects lightthen light which travels parallel to the axis of symmetry of a parabola and strikes its concave side is reflected to its focus, regardless of where on the parabola the reflection occurs.

Quadratic & Inverse Relationships

Conversely, light that originates from a point source at the focus is reflected into a parallel " collimated " beam, leaving the parabola parallel to the axis of symmetry.

The same effects occur with sound and other forms of energy. This reflective property is the basis of many practical uses of parabolas. The parabola has many important applications, from a parabolic antenna or parabolic microphone to automobile headlight reflectors to the design of ballistic missiles.