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

 Dec 3, 2015

Best Answer 

 #3
avatar+95177 
+5

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

 Dec 3, 2015
 #1
avatar
+5

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

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

 Dec 3, 2015
 #2
avatar+95177 
+5

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

 Dec 3, 2015
 #3
avatar+95177 
+5
Best Answer

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

Melody Dec 3, 2015

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