Quadratic equations - Assignment Example

Can you think of examples of processes that could be modeled with quadratic equations? In the real world, ‘Quadratic Equations’ can prove useful in a number of ways as –(1) Modeling costs for a general store –In C(x) = -0.03x2 + 57x + 310, for instance, the independent variable ‘x’ may refer to the number of materials bought which a store needs in order to produce sellable items. These materials are worth the variable cost C(x) with fixed cost of $310. Since the parabolic curve opens downward, as characterized by the negative leading coefficient, one manages to determine that a maximum cost is reached when x = -57/[ 2(-0.03) ]. The cost may be predicted to decline once the store decides to purchase materials greater than this value of ‘x’ on a regular basis.(2) Representing a profit function for a company –A maker of trophies observes that their profit behaves as P(x) = -0.

3x2 + fx – m where ‘f’ pertains to fee for designing awards according to client’s request while ‘m’ refers to the monthly studio rent. P(x) would then be the monthly profit obtained as a function of ‘x’ or the number of awards designed by the trophy – making company in a month. At a point where x = - f / [ 2(-0.3) ], maximum profit is achieved.(3) Estimating the velocity and the distance travelled by a projectile –Sports such as football often involve throwing of ball from the ground and the ball thrown (projectile) eventually follows a path of trajectory in the shape of a parabola.

Physicists characterize this scenario in a kinematic equation that is quadratic by nature, being y = V0y*t - ½ gt2 in which ‘y’ represents displacement of the ball whereas V0y is the initial velocity, along the vertical. If one wishes to find time ‘t’ when the ball hits the ground from the air, ‘y’ may be set to 0 so that ‘t’ may be solved given V0y, with g = 9.81 m/s2.