Final answer:
The factored form of a quadratic function is indeed used for quadratics and is expressed as f(x) = a(x - r₁)(x - r₂). The quadratic formula is a related but distinct method for finding the roots of a quadratic equation.
Step-by-step explanation:
The factored form of a quadratic function is expressed as f(x) = a(x - r₁)(x - r₂), where a is the leading coefficient and r₁ and r₂ are the roots of the quadratic equation. The factored form is very much suitable for quadratic functions, contrary to options A and D, which claim factored form is for linear equations or not applicable to quadratics. Within the factored form, solving for the roots of the equation becomes simpler because if either (x - r₁) or (x - r₂) equals zero, the entire equation equals zero, hence giving us the roots.
Option B states that the factored form helps find the vertex of a parabola, which isn’t directly accurate. To find the vertex of a parabola represented by a quadratic function, you would typically use the vertex form f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. However, the factored form can be used to find the x-coordinates of the vertex by averaging the roots r₁ and r₂.
Option C is regarding the quadratic formula, which is a separate method to find the roots of a quadratic equation ax² + bx + c = 0. The quadratic formula states that the solutions to the equation can be found using x = (-b ± √(b² - 4ac)) / (2a). While related, it is not the same as the factored form, but it can yield the same roots that would be used in the factored form.