Quadratic Equation Essay

Introduction Quadratic functions are more than algebraic curiosities—they are widely used in science, business, and engineering. The U-shape of a parabola can describe the trajectories of water jets in a fountain and a bouncing ball, or be incorporated into structures like the parabolic reflectors that form the base of satellite dishes and car headlights. Quadratic functions help forecast business profit and loss, plot the course of moving objects, and assist in determining minimum and maximum values. Most of the objects we use every day, from cars to clocks, would not exist if someone, somewhere hadn't applied quadratic functions to their design. We commonly use quadratic equations in situations where two things are multiplied together and they both depend of the same variable. For example, when working with area, if both dimensions are written in terms of the same variable, we use a quadratic equation. Because the quantity of a product sold often depends on the price, we sometimes use a quadratic equation to represent revenue as a product of the price and the quantity sold. Quadratic equations are also used when gravity is involved, such as the path of a ball or the shape of cables in a suspension bridge. Using the Parabola A very common and easy-to-understand application of a quadratic function is the trajectory followed by objects thrown upward at an angle. In these cases, the parabola represents the path of the ball (or rock, or arrow, or whatever is tossed). If we plot distance on the x-axis and height on the y-axis, the distance of the throw will be the x value when y is zero. This value is one of the roots of a quadratic equation, or x-intercepts, of the parabola. We know how to find the roots of a quadratic equation—by either factoring, completing the square, or by applying the quadratic formula. Let’s look at a throw made by a