Question

A) Express 10x-x^2-27 in form -(m-x)^2 +n

B) Hence show that 10x-x^2-27 is always negative


Thankyou

Answer 1

let's do it by completing the square

10x-x^2-27
= -x^2 + 10x - 27
= -(x^2 - 10x ..... ) - 27
= -(x^2 - 10x + 25 - 25) - 27
= -( (x-5)^2 - 25) - 27
= -(x-5)^2 + 25 - 27
= -(x-5)^2 - 2 -----> the form you wanted

argument:
(x-5)^2 is always positive
so
-(x-5)^2 is always negative
adding another -2 to a number already negative keeps it negative