urgent math
posted by Anne on .
complete the square to write each function in the form f(x)=a(xh)^2+k
f(x)=2x^220x3

2 x ^ 2  20 x  3
2 ( x ^ 2  10 x  3 / 2 )
2 ( x ^ 2  10 x + ?  3 / 2 ) + ?
The quantity to add is "the square of: (1/2) times the coefficient of the middle term 10"
That is:
[ ( 1 / 2 ) * (  10 ) ] ^ 2
(  5 ) ^ 2
2 ( x ^ 2  10 x  3 / 2 )=
2 [ x ^ 2  10 x + (  5 ) ^ 2  3 / 2 )  (  5 ) ^ 2 ]
2 [ x ^ 2  10 x + (  5 ) ^ 2 ]  2 * 3 / 2  2 * 25
x ^ 2  10 x + (  5 ) ^ 2 = ( x  5 ) ^ 2
2 * 3 / 2 = 3
2 * 25 = 50
2 [ x ^ 2  10 x + (  5 ) ^ 2  3 / 2 )  (  5 ) ^ 2 ] =
2 ( x  5 ) ^ 2  3  50 =
2 ( x  5 ) ^ 2  53
2 x ^ 2  20 x  3 = 2 ( x  5 ) ^ 2  53