Write the equation of a parabola with vertex (2,-1) and directrix y=-3.
Please show work and put your equation in graphing/vertex form.

  y = 1/8(x -2)^2 -1

Step-by-step explanation:

The vertex form of the equation of a parabola can be written as ...

  y = (1/(4p))(x -h)^2 +k

for vertex (h, k) and vertex-to-directrix distance p. Here, the vertex has a y-value of -1, and the directrix has a y-value of -3, so the distance between them is -1 -(-3) = 2, and the desired equation with vertex (2, -1) is ...

  y = 1/8(x -2)^2 -1

_____

Comment on the graph

One description of a parabola is that it is the locus of points equidistant from the focus and the directrix. I like to show that a point on the parabola (not the vertex) meets that requirement. That is what the dashed orange lines are for in the diagram. You can easily see that each has length 4.

a and c

step-by-step explanation:

he has now walked a total of what?

if i know what this is maybe i can

step-by-step explanation: