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A parabola is the representation of a quadratic equation in graph form and it can be seen in its many forms throughout the world. Not only does is dominate the mathematical and the physical world on very subtle levels, but we can also see the expression of quadratic equations in some forms of permanent architecture. For the purpose of accuracy, this explanation will demonstrate how a quadratic equation can be found in a simple action such as tossing a ball in the air.
When you throw a ball into the air, gravity forces the ball to slowly lose momentum as it climbs. As it reaches a point where the gravitational pull of the earth overpowers the velocity of the ball, also known as the vertex, depending on the force that it was thrown with in the first place, the ball has no choice but to return towards the earth from which it came. Upon dissecting the parabolic equation “(y = ax2 + bx + c )” , we can see that the c variable is the point from which the ball was thrown. The bx describes the rate at which the ball is thrown and the ax2 describes the force against the ball as it moves through the air. Therefore, a parabola depicting the ball being thrown from a specific height would show the amount of time before the ball returns to the ground as well as the maximum height the ball will reach during travel. In this case, the quadratic equation would be drawn as a downward opening parabola.
The representation of a quadratic expression is often referred to as a parabola, although the parabola itself is only a representation of the mathematical equation. To find a specific piece of architecture that represents the mathematical equation is inaccurate, but there are pieces of architecture that represent the parabola. The equation itself often has imaginary and infinite roots because the parabola represents an equation that can be changed depending on the circumstances; making it less of a geometric figure and more of a representation of an exercise in physics.
References
Parabolas. (n.d.). Retrieved May 16, 2016, from California State University Northridge: http://www.csun.edu/~ayk38384/notes/mod11/Parabolas.html
