completing the square help w/ y = -4/5x^2 + 12x - 8

[tinykitkatgrl]

Find the standard form ( y=a(x-h)^2+k) of the equation y = -4/5x^2 + 12x - 8.

I know I have to complete the square, but completing the square confuses me so much. Help, anyone?

 

[arthur ohlsten]

step 1 isolate the x terms
y=[-4/5 x^2+12x] -8 factor out -4/5
y=-4/5[x^2-60/4 x] -8
y=-4/5[x^2-15x ]-8
complete the square by adding and subtracting 1/2 the x coefficient squared
y=-4/5 [x^2-15x+ 225/4] +45 -8
[-4/5 times 225/4]=-45 so we added -45 inside the paranthesis and 45 outside

y=-4/5[x-15/2]^2 +37 a parabola
open down vertex at 15/2,37
axis of symmetry x=15/2

please check my algebra
Arthur