What is the parabola of the graph below?

Question

Directrix x=-2 

focus = (-4,-4) 

i Don’t have a picture of the graph 

Answer 1

Since the directrix is a vertical line, the axis of the parabola is horizontal and passes through the focus.  

 

So, the axis is the horizontal line y = -4.  The vertex lies on the axis and is halfway between the focus and directrix.  So the vertex is (-3,-4).  The focus is inside the arc of the parabola, so the parabola opens leftward.

 

Equation of parabola has the form:  (y - (-4))² = -4p(x - (-3))

 

                                                    (y + 4)² = -4p(x + 3)

 

p is the distance from the focus to the vertex.  So, p = 1.

 

Equation of parabola:  (y+4)² = -4(x+3).