A parabola can be drawn given a focus of ( 4 , 4 ) (4,4) and a directrix of y = − 2 y=−2. What can be said about the parabola?

Question

Find Parabola Features without Graph

Answer 1

Already asked and answered.

Answer 2

V(4,1)

[[dyslexic error corrected]]

Opens upward

One can even find its equation!

Answer 3

Note, the vertex will have the same x coordinate as the focus

and be at the midpoint between focus and directrix.  The

midpoint of (4, 4) and (4, -2) is:  ((4+4)/2, (4-2)/2) = (4, 1)

 

The parabola opens around the focus in a direction away from the

directrix, so it opens upward.  In format y = ax² +bx + c for a

parabola opening upward, a>0.

 

So we know the parabola opens upward from a vertex at (4, 1)

and is form  y = ax² + bx + c with a>0