Final answer:
The question covers quadratic equations, which can be written in vertex or standard form. Vertex form is y = a(x - h)^2 + k and is useful for finding the vertex, while standard form ax^2 + bx + c = 0 is typically better for finding the roots using the quadratic formula.
Step-by-step explanation:
The question pertains to the forms in which a quadratic equation can be expressed: vertex form and standard form. A quadratic equation is an equation of the second degree, meaning it includes at least one term that is squared. The standard form of a quadratic equation is written as ax^2 + bx + c = 0, where a, b, and c are constants, and a is not equal to 0.
The vertex form of a quadratic equation, on the other hand, is written as y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola described by the equation. Each form has its benefits; for example, the vertex form makes it easy to determine the vertex of the parabola, which can be useful in graphing or solving optimization problems. The standard form is more beneficial when using the quadratic formula to find the roots of the equation or when applying the method of completing the square.