The equation of a parabola is given. y=12x2+6x+24 what is the equation of the directrix of the parabola?

the equation of a parabola is (y−1)2=16(x+3) .
what is the equation of the directrix of the parabola?

1.) Given the equation of a parabola


The vertex form of a parabola is given by

where: (h, k) is the vertex and p is the distance between the vertex and the directrix.



From the equation, the vertex is and the distance between the vertex and the directrix is 3.

Because, the x-part of the equation is squared and the value of p is positive, this means that the parabola opens up and the directrix is a horizontal line having the value y = c, where c is the y-value of the vertex - 3

Equation of the directrix is

Therefore, the equation of the directrix is

2.) Given the equation of a parabola written in vertex form


The vertex form of a parabola is given by

where: (h, k) is the vertex and p is the distance between the vertex and the directrix.



From the equation, the vertex is and the distance between the vertex and the directrix is 4.

Because, the y-part of the equation is squared and the value of p is positive, this means that the parabola opens to the right and the directrix is a vertical line having the value x = c, where c is the x-value of the vertex - 4

Equation of the directrix is
Therefore, the equation of the directrix is

Hope i can you!