To apply the quadratic formula to a particular quadratic equation just convert the equation to standard form and substitute the appropriate values. The focus of Secondary Mathematics II is on quadratic expressions, equations, and functions and on comparing their characteristics and behavior.This process is called completing the square. When would I use the Quadratic Formula? Free lesson on Investigation: Deriving the quadratic formula, taken from the Quadratics topic of our Utah Core Standards (2016) Math II textbook. If the discriminant is equal to zero, the two roots will be real and equal to each other;. 3. Discriminant. Do you see b2 − 4ac in the formula above? Objective 3: Solve and graph quadratic equations. a. Write this as an equation which you can solve in the form t = f(u,g,s), where f is some function of u, g and s.