Final answer:
The quadratic formula is used to find the roots of a quadratic equation, which can be graphed as a parabola on a two-dimensional plane. When constructed from physical data, these equations typically have real roots, with the positive ones being more significant.
Step-by-step explanation:
The quadratic formula calculates the roots of a quadratic equation and indicates the nature of its graph. A quadratic equation of the form ax²+bx+c = 0 can be solved for its roots using the quadratic formula, which is derived from the process of completing the square and is given by x = (-b ± √(b²-4ac))/(2a). These roots can be real or complex numbers. When considering quadratics constructed on physical data, such as those occurring in projectile motion or structure stress analyses, the roots tend to be real, and it is often the positive root that has physical significance.
Additionally, the concept of Two-Dimensional (x-y) Graphing is important as quadratic equations graph as parabolas, and the properties of these parabolas are related to the sign and magnitude of the a, b, and c terms within the equation. The vertex of the parabola represents the maximum or minimum point, and the x-intercepts represent the roots of the equation.