Posted by Zoey on .
for the conic y=5x^240x+78 find an equation in standard form and its vertex, focus, and directrix

PreCalc 
Reiny,
complete the square
y = 5(x^2  8x + ....) + 78
= 5(x^2  8x + 16  16) + 78
= 5( (x4)^2  16) + 78
= 5(x4)^2  80 + 78
= 5(x4)^2  2
take over .... 
PreCalc 
Zoey,
What's my next step??

PreCalc 
Reiny,
We could write our answer in the form
y+2 = 5(x4)^2
take a look at
http://jwilson.coe.uga.edu/emt725/class/sarfaty/emt669/instructionalunit/parabolas/parabolas.html
halfway down the page at example 3
and follow the steps. 
PreCalc 
Zoey,
thank you!