Rewrite the function by completing the square.
g(x) = 2x^2 – 7x + 5
g(x) =...(x+...)^2+...

2(x - )² -

Step-by-step explanation:

Given

2x² - 7x + 5

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

= 2(x² - x ) + 5

To complete the square

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

= 2(x² + 2(- )x + - ) + 5

= 2(x - )² - + 5

= 2(x - )² -

= 2(x - )² -

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

Step-by-step 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.