grafik fungsi y= (m-2)x^2 -6x +3m selalu diatas sumbu x. batas batas nilai m yang memenuhi adalah

Diatas sb x
a > 0, D < 0

a = m-2
b = -6
c = 3m
D = b²-4ac
= 36-4(m-2)(3m)
= 36-12m²+24m
= -12m²+24m+36

a > 0
m-2 > 0
m > 2

D < 0
-12m²+24m+36 < 0
---------------------------- :-12
m²-2m-3 > 0
(m-3)(m+1)
m = 3 dan m = -1

___ -1 ____ 3____

m = 0, 0²-2(0)-3 = -3

+++++ -1 ----- 3 ++++-
m < -1 dan m > 3

Hp {m > 3 }