-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.

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.

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

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

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

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)

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

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..

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 (http://www.padowan.dk)