Given the directrix of y = −1 and focus of (0, 3), which is the equation of the parabola?

(0,3) , y−3 Since the directrix is vertical, use the equation of a parabola that opens up or down.   (x−h)2=4p(y−k)

Find the vertex.

The vertex (h,k) is halfway between the directrix and focus. Find the y coordinate of the vertex using the formula y=y coordinate of focus+directrix2. The x coordinate will be the same as the x coordinate of the focus.(0,3−32)

Simplify the vertex.

Subtract 3 from 3.(0,2) Divide 0 by 2.(0,0) Find the distance from the focus to the vertex.

The distance from the focus to the vertex and from the vertex to the directrix is |p|. Subtract the y coordinate of the vertex from the y coordinate of the focus to find p.p=−0Subtract 0 from 3.p=3

Step-by-step explanation:

1.  f(0,3)                         directrix=y=1       Also, find the vertex.

2.  Draw what you know on a graph:      y=1  is a line parallel to the X-axis and going through the point (0,1).

The focus is at (0,3) above the directrix.   The vertex should be above the focus point and half way the distance from the directrix line and the focus point.    Using y values you can say the total distance is 3-1=2 units   Then half of that would be one unit.  Therefore, the vertex is at (0, 2), which is in the middle distance of the directrix and the focus point.

3.  The parabola is going to open upwards because the parabola will open away from the directrix. Also, the p=distance from vertex to focus is +1 unit upward, so p= +1.

4.  Use this standard equation:  (X-h)2 = 4p(y-k).     V(h,k)=(0,2)    h=0    and k=2.

5.       (X-0)2 =  4(1)(y-2)                   X2 =4(y-2)                  Answer

w > -20

Step-by-step explanation:

w/5 > -4

w > -4 x 5

w > -20