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mizzqueen1 · Apr 27, 2008, 08:08 AM

-4(y+2) = (x-3)^2

I need help finding the vertex, axis, p, focus, and directrix. I'm so blanked out.I cannot remember anything.

galactus · Apr 27, 2008, 10:33 AM

This is a parabola with equation $(x-3)^{2} = -4(y+2); \;\ y=\frac{-x^{2}}{4}+\frac{3}{2}x-\frac{17}{4}$

It has the form $(x-h)^{2}=4p(y-k)$

Where h and k are the coordinates of the vertex.

It has vertex at (3,-2) and is concave down.

You were wondering what 'p' represented. That is the distance from the focus to the vertex. $p=\frac{1}{4a}$

To find the focus and directrix of this parabola:

It has the form $y=ax^{2}+bx+c$ .

In this case $a=\frac{-1}{4}$ , where $p=\frac{1}{4a}=\frac{1}{4(\frac{-1}{4})} = -1$

Thus, the parabola opens downward and has focus $(3, -3)$

The directrix is the horizontal line $y = -1$ , which is a distance 1 from the vertex.

galactus · Apr 27, 2008, 10:40 AM

I made a mistake on the graph. The directrix should read y = -1.

redtown · Jul 15, 2010, 12:53 PM

identify the vertex, focus and the directrix of y=1/24x^2

redtown · Jul 15, 2010, 12:55 PM

identify the vertex, focus and the directrix of y=1/24x^2

galactus · Jul 15, 2010, 02:19 PM

Please start your own thread. Piggy backing on an old thread is not a good idea.

Notice that it has the form $y=ax^{2}$ .

Since 1/24 is positive, the parabola is concave up and has vertex at the origin.

$a=\frac{1}{24}$ .
$a=\frac{1}{4p}$

$\frac{1}{24}=\frac{1}{4p}$

Solve for p. p is the distance from the vertex to the focus and from the vertex to the directrix.
The directrix has equation y=-p and the focus has coordinates (0,p)

xjessy217x · Jul 19, 2010, 08:12 PM

x^2 = -36y what is the directrix?

MR.Woman · Sep 12, 2010, 07:24 AM

solving for directrix?

1st, you must find the axis in equation x^2 = 4ay, then divide -36 by -4 by the process of canceling.. The answer is 9.. therefore a=9 (the axis is 9)..

2nd you must find the focus.. then you can now solve for the directrix..

galactus · Sep 12, 2010, 07:40 AM

Originally Posted by xjessy217x

x^2 = -36y what is the directrix?

This is a parabola with vertex at the origin and concave down.

As Mr. Woman pointed out, p=9.

Thus, the directrix is 9 units from the vertex.

To see it, graph $y=\frac{-x^{2}}{36}$ on a calculator or some other software.

If you do not have a calculator, go here and download the free graphing utility.

Graph