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Graph Of A Parabola Related To Its Quadratic Function: Explain In Detail

Referencing Styles : Harvard | Pages : 1

In the field of mathematics, a parabola is usually referred to a plane curve that is symmetrical in the mirror form and closely approximate to U-shaped. It can be fitted into several of the superficially present mathematical descriptions, which can again be utilized to prove exactly the same curves.

One description related to a parabola involves a point, which is commonly called a focus and a line, which has the name of a directrix. The parabola refers to the locus of the points within that plane which lie at an equal distance from both the directrix and the focus. The parabola carries another description which states that, it is a conic section, which is created by the intersection of a right circular cone shaped surface and a plane which is again parallel to some other plane that is a tangent to the particular conical surface. The line which is perpendicular to the directrix and which passes through the focus is known as the “axis of symmetry”. The point upon the parabola that intersects the axis is called the vertex, and is also the point on the parabola which is sharply curved. The line of distance between the vertex and the focus which is calculated along the axis is referred to as the focal length. The “latus rectum” is the line of chord within the parabola which is exactly parallel to the existing directrix and also, passes right through the focus. Parabolas can open up in any direction be it right, left, up and down or maybe in some other unspecific direction. The parabolas find their applications in many of the fields such as parabolic antenna or the parabolic microphone to implement its application in the headlight reflectors and also the design of the ballistic missiles which is on a larger scale. Any parabola can be changed in shape or size to be exactly placed upon any other parabola to coincide it.

Generally, the graph of a quadratic equation is,

f(x)=ax2+bx+c

Here, the graphs of the quadratic function are called the parabolas.

Finding the intercepts is certainly a common process. To find the y-intercept of a parabola, y=f(x), all that needs to be done is set x=0 and then evaluation is done to find the y coordinate. In other words, the y-intercept is the point referred as (0, f(0)). The finding of the x-intercepts is calculated in a similar manner. In here, the y is set equal to zero and the resulting equation is solved for the x coordinates. So the solving of the equation is,

f(x)=0.

A quadratic function carries the form of the equation which states that, f(x) = ax2 + bx + c, in which a, b and c are numbers which are not equal to zero. The graph related to this quadratic equation is a curve which is commonly referred to as parabola. A parabola intersects its own axis which defines the symmetry at a specific point of the parabola. The two points together form a line when joined.

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