Question

Determine the orientation of the parabola.
directrix: x= -4; p=-3
Please help!!

Answer 1

Horizontal parabola, oriented to the negative side.

Explanation:

Givens

The directrix is
`x=-4` and
`p=-3`

Now, if the directrix has the form
`x=-p`, it means the directrix is vertical and the parabola is horixontal.

Its equation would have the form
`y^(2) =4px`.

Now, is
`p<0`, the parabola would open to the negative side, and its equation is

`y^(2) =4(-3)x\\y^(2) =-12x`

Therefore, the parabola is draw towards the negative numbers of horizontal axis.

The image attached shows the direction of the parabola.

Answer 2

see explanation

Explanation:

Since the directrix has equation x = - 4, that is a vertical line

This indicates that the parabola is horizontal

Since p = - 3

This indicates the parabola opens to the left.

The parabola is horizontal and opens to the left.