Final answer:
Completing the square is an important algebraic method for solving quadratic equations and can aid in graphing. Quadratic formulas are widely used in fields like physics and economics to predict outcomes and model situations. They are essential for finding roots and critical points.
Step-by-step explanation:
Understanding completing the square is important because it is a method used for solving quadratic equations, which are second-order polynomials. This algebraic technique allows us to convert a quadratic equation into a perfect square trinomial, which can then be solved easily by taking the square root of both sides. The method is beneficial, especially when the equation cannot be factored easily or when we need to derive the vertex form of the equation for graphing purposes.
Quadratic formulas are essential in various applications, such as calculating projectile motion in physics, analyzing profit and cost functions in economics, and determining rates of change in calculus. Solving for the roots of quadratic equations provides critical points that are used in different fields to predict outcomes, optimize solutions, and model real-world situations.