Question

Find an equation of a parabola with a vertex at the origin and directrix y = –2.5

Answer 1

Any selections .-.

Answer 2

http://prntscr.com/316nrc

Answer 3

y = 1/6x^2

Answer 4

With those options, we can use two facts.
(a) The focus is always "inside" the parabola's concave section, while the directrix is behind it.
(b) The directrix is negative and horizontal (all y-values are -2.5), which means it is below the vertex (0,0) so that the graph has to look like this

This would be a logical guide for this problem that does not need much gritty algebra to do. This parabola just looks like y = ax^2 with positive a.

Answer 5

o.O did i get that wrong @AccessDenied

Answer 6

1/6x^2 wasn't an option? D:
although the sign and form was correct for sure

Answer 7

Ohhhh ok thanks for telling me lol :p

Answer 8

There was also an expression for the a in y = ax^2 in terms of the distance to the focus/directrix that was like:
a = 1/(4|c|)
The directrix would again say that the parabola is facing upwards, thus having positive coefficient.
My memory is a bit fuzzy on those equations though.

Answer 9

I still dont get this >(

Answer 10

*:(

Answer 11

Same @AccessDenied

Answer 12

Is there a specific part that does not make sense? I can try to explain better that part, else I'll take it from the top. :p

Answer 13

umm maybe you can just take it from the top if its not too much trouble for you?

Answer 14

No worries.

The definition of a parabola using its focus and directrix is:
The set of all points that are an equal distance between the point (focus) and line (directrix).
Do you know of that definition?

Answer 15

yes

Answer 16

So, we know that the point (0,0) is on the parabola. It is an equal distance from the directrix (y=-2.5) as it is from the focus, which we don't know yet.