Linear and quadratic equations in real-world applications

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