Final answer:
Carol was provided with the vertex point (-3, 2) of the parabola and the fact that it opens downward due to the negative coefficient before the parenthesis in her equation. The directrix would be a horizontal line above this vertex, but its exact equation cannot be determined from the given information.
Step-by-step explanation:
The equation −2(x+3) = (y−2)2 Carol wrote is a parabola in vertex form, which is typically written as (y - k) = a(x - h)2, where (h, k) is the vertex point and 'a' determines the direction and width of the parabola. From her equation, we can deduce that the vertex point she was given is (-3, 2), since those are the values that make each binomial zero.
The equation given in the question −2(x+3)=(y−2)² represents a parabola. To determine the information provided to write this equation, we can compare it to the standard equation of a parabola: y = ax² + bx + c.
From the given equation, we can deduce that the vertex point is (-3, 2), the direction of opening is upwards, and the directrix is a horizontal line passing through the point (0, 0). Therefore, the information provided to write the equation is: vertex point, direction of opening, and directrix.
The negative coefficient in front of the parenthesis indicates that the parabola opens downward since 'a' is negative. The information about the directrix is not explicitly given in the equation, but if the parabola opens downwards, and we know the vertex, the directrix must be a horizontal line above the vertex. As it stands, we cannot directly determine the directrix equation without additional information.