Parabola Help

I just had a quick look at that site our guest sent you to.

It looks quite good for checking answers.

I doubt that it explains the answers, although I did not actually use it so I could be wrong.

But sites for checking answers can be very useful too :)

Thanks guest #1

Go online to this calculator. I believe it will solve your problem:

http://www.endmemo.com/geometry/parabola.php

Find the vertex, focus, and directrix equation of y = x2 – 6x – 8.

You need to get your equation in the form  $(x-h)^2=4a(y-k)^2$

where (h,k) is the vertex and a is the focal length.

Now I can see straight of that this is a concave up parabola.

That is helpful because that tell me that the focus is above the vertex and the directrix is below it.

$y=x^2-6x-8\\ x^2-6x=y+8\\ \mbox{Now complete the square}\\ x^2-6x+9=y+8+9\\ (x-3)^2=y+17\\ (x-3)^2=4*\frac{1}{4}(y+17)\\ so\\ Vertex=(3,-17)\\ focal \;length = 0.25\\ focus: x=3, y=-17+0.25=-16.75\qquad (3,-16.75)\\ directrix: y=-17-0.25 = -17.25 \qquad y=-17.25\\ $

Here is the graph

https://www.desmos.com/calculator/yylyzk2bdj