Question

Rewrite the function by completing the square.

g(x) = 2x^2 – 7x + 5
g(x) =...(x+...)^2+...

Answer 1

g(x) = 2(x - 1.75)^2 - 1.125.

Explanation:

g(x) = 2x^2 – 7x + 5

First take the 2 out of the first terms:

g(x) = 2(x^2 - 3.5x) + 5

Now complete the square on the expression in the parentheses:

g(x) = 2 [ (x - 1.75)^2 - 1.75^2] + 5

g(x) = 2 [ (x - 1.75)^2 - 3.0625] + 5

g(x) = 2(x - 1.75)^2 - 6.125 + 5

g(x) = 2(x - 1.75)^2 - 1.125.

Answer 2

2(x -
`(7)/(4)` )² -
`(9)/(8)`

Explanation:

Given

2x² - 7x + 5

The coefficient of the x² term must be 1, thus factor out 2 from 2x² - 7x

= 2(x² -
`(7)/(2)` x ) + 5

To complete the square

add/ subtract ( half the coefficient of the x- term )² to x² -
`(7)/(2)` x

= 2(x² + 2(-
`(7)/(4)` )x +
`(49)/(16)` -
`(49)/(16)` ) + 5

= 2(x -
`(7)/(4)` )² -
`(98)/(16)` + 5

= 2(x -
`(7)/(4)` )² -
`(18)/(16)`

= 2(x -
`(7)/(4)` )² -
`(9)/(8)`