The quadratic formula is one way to solve the quadratic equation. Although other, often easier, ways to solve the quadratic equation exist, including factoring, graphing and completing the square, the quadratic formula is the only option that always works.
The quadratic formula solves the quadratic equation, which is:
ax2 + bx + c = 0
The quadratic formula does this by altering the quadratic equation to allow users to solve for x directly.
Though it can take time to solve, the quadratic formula is the only method for solving quadratic equations that works every time. It also holds key advantages over other methods. For example, unlike completing the square, there are no complex steps that users must remember. To solve the quadratic equation, users simply plug in the coefficients and solve the problem.
Like all quadratics, the quadratic formula offers users two solutions, one positive and one negative. Solutions also may or may not be real or complex.
There are several applications of the quadratic equation, and thus uses for the quadratic formula, in the real world. For example, when throwing a ball, it follows a distinct line up into the air, slowing as it moves and eventually comes down again and lands on the ground. With the height (a) and velocity (b) of the throw along with gravitational pull (c) as constants, the quadratic formula tells users when (x) the ball will finally fall to the ground.