Question

complete the square to write each function in the form f(x)=a(x-h)^2+k
f(x)=2x^2-20x-3

Answer 1

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