inear equations -- as shown by line graphs -- are used to describe two quantities that are directly proportional with each other by some amount. An example of this is the formula for computing distances and speed. The distance traveled by an object is directly related to its speed. The faster it moves, the farther it goes. The formula for computing the distance is D = S*T where'd = distance, S = speed, and T = time. For example, a person walking at a constant speed of 4 feet/second will traverse the distance for each second that passes:
Parabola
Parabolas are produced using quadratic equations of the form y = Ax^2 + Bx + C. A real life example is the formula for acceleration: s = ut + 1/2(at^2), where'd = distance, t = time, and a = average acceleration. The distance traveled is proportional to the square of the time. Another interesting example is the path of an object thrown upward. It will travel up and fall down along a parabolic path as described by the equation y = v0t - 1/2 gt^2, where v0 is the initial velocity, g is the acceleration due to gravity (9.8 meters/s^2), and t is the time elapsed in seconds. For example, an object is thrown at 9 meters per second. The path it will travel is described by the following graph:
3.Hyperbola
Hyperbolas are produced using equations of the form (x - h)^2/a^2 - (y - k)^2/b^2 = 1. There are various examples of hyperbolas in real-life. Two stones thrown in a pool of water will produce ripples of concentric circles. The intersection of these circles form hyperbolas. This property is being used by radars to pinpoint the location of an object. The path of a comet as it passes by the earth is also a hyperbola. In physics, the relationship between the volume and pressure of a gas (with constant temperature) is inversely proportional and has the shape of a hyperbola when plotted.
4.Exponential
Exponential functions have the form y = a^x, where a and x are real numbers. These functions can be found in real-life situations such as computation of compound interests, radioactive decay, and population growth.
Bibliography
Budd, Chris and Sangwin, Chris. "101 Uses of a Quadratic Equation: Part II." Retrieved May 22, 2006 at http://plus.maths.org/issue30/features/quadratic/index-gifd.html
Hyperbola." Retrieved May 22, 2006 at http://www.punahou.edu/acad/sanders/geometrypages/GP20Hyperbola.html
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