Sections: Introduction, Finding information from the equation, Finding the equation from information, Word problems & Calculators

In algebra, dealing with parabolas usually means graphing quadratics or finding the max/min points (that is, the vertices) of parabolas for quadratic word problems. In the context of conics, however, there are some additional considerations.

To form a parabola according to ancient Greek definitions, you would start with a line and a point off to one side. The line is called the "directrix"; the point is called the "focus". The parabola is the curve formed from all the points (x, y) that are equidistant from the directrix and the focus. The line perpendicular to the directrix and passing through the focus (that is, the line that splits the parabola up the middle) is called the "axis of symmetry". The point on this axis which is exactly midway between the focus and the directrix is the "vertex"; the vertex is the point where the parabola changes direction.

"regular", or vertical, parabola (in blue), with the focus (in green) "inside" the parabola, the directrix (in purple) below the graph, the axis of symmetry (in red) passing through the focus and perpendicular to the directrix, and the vertex (in orange) on the graph

"sideways", or horizontal, parabola (in blue), with the focus (in green) "inside" the parabola, the directrix (in purple) to the left of the graph, the axis of symmetry (in red) passing through the focus and perpendicular to the directrix, and the vertex (in orange) on the graph

The name "parabola" is derived from a New Latin term that means something similar to "compare" or "balance", and refers to the fact that the distance from the parabola to the focus is always equal to (that is, is always in balance with) the distance from the parabola to the directrix. In practical terms, you'll probably only need to know that the vertex is exactly...

...Conics are surprisingly easy! There are four types of conic sections, circles, parabolas, ellipses, and hyperbolas. The first type of conic, and easiest to spot and solve, is the circle. The standard form for the circle is (x-h)^2 + (y-k)^2 = r^2. The x-axis and y-axis radius are the same, which makes sense because it is a circle, and from
In order to graph an ellipse in standard form, the center is first plotted (the (h, k)). Then, the x-radius is plotted on both sides of the...

...
The Parabola
What is a Parabola?
A quadratic expression is an expression in which the highest power of is 2. Consider the following:
The above equations are all quadratic expressions as the highest power of is 2. When a quadratic function is graphed, the resulting curve is called a parabola, as demonstrated in figures 1 and 2.
Real Life Application
A quadratic function and parabola can be used when undertaking a new...

...A parabola is a two-dimensional, mirror-symmetrical curve, which is approximately U-shaped when oriented as shown in the diagram, but which can be in any orientation in its plane. It fits any of several superficially different mathematical descriptions which can all be proved to define curves of exactly the same shape.
One description of a parabola involves a point (the focus) and a line (the directrix). The focus does not lie on the directrix. The locus of...

...DE be a line perpendicular to this triangle, cutting BG in H. Let the cone be cut by a plane through DE parallel to AG, so that the intersection with the cone will be the curve called the parabola. Let Z be the point where this curve cuts AB. Then the line ZH is called by Apollonius the diameter of the parabola, or the principal diameter, or the diameter from generation; it is now called the axis. From Z draw ZT at right angles to ZH and in the plane of ZH and AB,...

...Goodman
Pre-AP Algebra 2
Coach Crowder
February 22, 2013
Analysis
When thinking of video games you don’t think about math at all. The two things just seem so far apart that they can’t be together. In all reality video games are filled with math. Parabolas are more common in video games than most people really notice. As mentioned before Mario is one of the most popular games ever to be created. When created it looked like a simple game about a plumber trying to save a...

...Theory of Parabolas
By Amergin McDavid
A parabola is designed on a basic formula, Y=ax^2+bx+c, which allows it to achieve a curve not seen in a normal line graphed using a Y=mx+b format. To the left is a graph who’s formula is y=x^2, where a=1, b=0, and c=0. I have isolated the (a) factor to see its effects on the parabola.
Below is a graph where I have changed the (a) multiple times.
The result is that as the (a) decreases, the mouth of the...

...The Importance of the Parabola
What exactly is a parabola? Well it could quite possibly be the most powerful shape that our world has ever known. It is used in many designs since it is so sturdy and powerful. Countless structures and devices use the parabola and it does nothing but enhance whatever it is used in. What makes it so powerful? Just keep reading and find out.
Used in bridges, doors and buildings, the shape of the parabola...

...The Parable of the Sadhu
The following case first appeared in the September-October 1983 issue of the Harvard Business Review. It was written by business professor Bowen H. McCoy and is a true story
----------------------------------------
The Nepal experience was more rugged than I had anticipated. Most commercial treks last two or three weeks and cover a quarter of the distance we travel.
My friend Stephan, the anthropologist, and I were halfway through the 60-day himalayan part of the...