Go online to this calculator. I believe it will solve your problem:
http://www.endmemo.com/geometry/parabola.php
+118609 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
+118609 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
