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Turn 7y-4=8x^2-24x into the form y=a(x-h)^2+k to solve a parabola and its vertex, focus, directrix, and the axis of symmetry.

Mathematics
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hey, how's it going?
good, just a lil stressed trying to find the solution to this problem
ok so we want to get the right side looking like a(x-h)^2

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Other answers:

yep, i was thinking to add 4 to both sides and then factor out an 8
ok, that works, 7y = 8 (x^2 - 3x) + 4
so to end up with the -3x term, we are going to need (x-3/2)^2
but (x-3/2)^2 = x^2 -3x + 9/4, so we have to subtract that 9/4 from the right side of the equation since we added it to "complete the square"
ok, so then it would be 7y - 9/4 = 8 (x - 3/2)^2 +4 so i wouldn't need to add the 4 on both sides in the first place?
no, we added 9/4 to the right side, so we need to add it to the left side (or subtract it to the right)
oh, sorry i meant + 7y + 9/4 = 8 (x - 3/2)^2 +4 7y = 8 (x - 3/2)^2 + 7/4 so it would end up like that?
then we would divide it by 7 on both sides
i'm sorry, i made a mistake we actually added 8*9/4
so instead of 9/4 added to the left side, it would be 8(9/4) = 18
because we didn't just add 9/4, we added 9/4 inside of parentheses multiplied by 8
okay so then it would be 7y = 8 (x - 3/2)^2 - 14 ?
looks good
final thing is gonna be y = 8 (x - 3/2)^2 - 2
don't forget to divide the 8 by 7
opps my bad y = 8/7 (x - 3/2)^2 - 2 thanks so much

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