Question

-

Express x^2 – 5x + 8 in the form (x – a)^2 + b
where a and b are top-heavy fractions.



i got (x-5/2)^2- 7/4
can someone tell me where i’m going wrong please :/

Answer 1

(x -
`(5)/(2)` )² +
`(7)/(4)`

Explanation:

x² - 5x + 8

Using the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² - 5x

x² + 2(-
`(5)/(2)` )x +
`(25)/(4)` -
`(25)/(4)` + 8

= (x -
`(5)/(2)` )² -
`(25)/(4)` +
`(32)/(4)`

= (x -
`(5)/(2)` )² +
`(7)/(4)`