ATQ's
express 4x^2 - 12x + 11 in the form a(x+b)^2 +c and hence write down:
(i) the minimum value of 4x^2 - 12x + 11
(ii) the maximum value of
1(over)
4x^2 - 12x + 11
thanks
as an aside
^2 is supposed to be squared
and (ii)is a fraction not very good at this web stuff
express 4x^2 - 12x + 11 in the form a(x+b)^2 +c
4x^2 - 12x + 11 = 4(x^2 - 3x) + 11
Comparing x^2 - 3x with the identity
x^2 + 2px = (x + P)^2 - p^2
we can match the left-hand sides by putting
2p = -3; that is p = -3/2
Putting this value also into the right-hand side, we obtain the completed-square form
x^2 - 3x = (x - 3/2)^2 - (-3/2)^2 = (x - 3/2)^2 - 9/4
Hence 4(x^2 - 3x) +11 = 4(x - 3/2)^2 - 9/4) + 11
= 4(x - 3/2)^2) - (9/4 *4) + 11
= 4(x - 3/2)^2 - 9 + 11
So the required form is 4(x 3/2)^2 + 2