Question

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.

Answer 1

hey, how's it going?

Answer 2

good, just a lil stressed trying to find the solution to this problem

Answer 3

ok so we want to get the right side looking like a(x-h)^2

Answer 4

yep, i was thinking to add 4 to both sides and then factor out an 8

Answer 5

ok, that works, 7y = 8 (x^2 - 3x) + 4

Answer 6

so to end up with the -3x term, we are going to need (x-3/2)^2

Answer 7

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"

Answer 8

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?

Answer 9

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)

Answer 10

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?

Answer 11

then we would divide it by 7 on both sides

Answer 12

i'm sorry, i made a mistake we actually added 8*9/4

Answer 13

so instead of 9/4 added to the left side, it would be 8(9/4) = 18

Answer 14

because we didn't just add 9/4, we added 9/4 inside of parentheses multiplied by 8

Answer 15

okay so then it would be 7y = 8 (x - 3/2)^2 - 14 ?

Answer 16

looks good

Answer 17

final thing is gonna be
y = 8 (x - 3/2)^2 - 2

Answer 18

don't forget to divide the 8 by 7

Answer 19

opps my bad y = 8/7 (x - 3/2)^2 - 2
thanks so much