Aparabola, with its vertex at the origin, has a directrix at y = 3. which statements about the parabola are true? check all that apply.
the focus is located at (0,–3).
the parabola opens to the left.
the p value can be determined by computing 4(3).
the parabola can be represented by the equation x2 = –12y.
the parabola can be represented by the equation y2 = 12x.

Answer :- 1.The focus is located at (0,–3).

4.The parabola can be represented by the equation x2 = –12y.

Explanation:-

Given:- A parabola, with its vertex at the origin, has a directrix at y = 3.

⇒ the parabola is symmetric to the y -axis and opens to the downwards as it opens opposite to the directrix.

and focus is located at (0,-3) as for directrix y=a focus =(0,-a)

⇒The parabola can be represented by the equation with a=3

p=distance between the vertex and focus=|-3-0|=3 units

Thus options 1, 4 are correct.

m = undefined

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

If the slope m was equal to 0, then it would be a horizontal line rather than a vertical line.

Using the Vertical Line Test, we also know that the graph is not a function.

Usually a vertical line has an undefined slope, as x equals a certain number, and m = unknown.