Why is solving the equation using the quadratic formula more helpful with a quadratic equation that can be written in vertex form or in standard form.

Answer 1

Solving a quadratic equation using the quadratic formula is equally effective regardless of whether the equation is in standard form or vertex form. The quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a), allows us to find the solutions for any quadratic equation of the form ax² + bx + c = 0.

The advantage of using the quadratic formula is that it gives a straightforward and systematic approach to finding the solutions of a quadratic equation. It works in all cases, providing exact solutions even for complex or irrational roots.

Whether an equation is in standard form (ax² + bx + c = 0) or vertex form (a(x - h)² + k = 0) does not affect the applicability or effectiveness of the quadratic formula. In fact, regardless of the equation's form, the quadratic formula can be used to find the solutions by identifying the values of a, b, and c in the equation.

In practice, converting an equation from vertex form to standard form before applying the quadratic formula might offer some simplification, but this step is not necessary as the quadratic formula can be used in either case. Ultimately, the quadratic formula is a powerful and versatile tool for solving quadratic equations, and it proves helpful regardless of whether the equation is in vertex form or standard form.