Question

Help please.
Write the equation of a parabola with vertex at the origin and directrix y=-6. Show your steps.

Answer 1

@Aveline @IconForHire56 @knesha

Answer 2

The standard equation of a parabola is:
\[(x-h)^{2}=4p \times (y-k)^{2}\]
The directrix is:
\[y=k-p\]
And the focus is:
\[(h, k + p)\]

(h,k) is the vertex

Answer 3

\[(x – h)^{2}= 4p \times (y – k) \]
Let's plug in (0,0) for the vertex since the vertex is at the origin:
\[x ^{2}=4p \times y\]
The directrix is -6 units away from the vertex, so p=6
\[x ^{2}=24y\]

Answer 4

I noticed I made an error on my first post:
The standard equation is \[(x-h)^{2}=4p \times (y-k)\]

Answer 5

Ok thanks .

Answer 6

sorry i got called away
in any case you had great help

Answer 7

the parabola will open upwards with the focus at y=6

Answer 8

ok.

Answer 9

https://www.desmos.com/calculator/6brcymnbly

there it is

Answer 10

Is X^2=24Y the answer?