Question 556504: f(x)= -4x^2-8x+3
is this a minmum or a maximum
what is the value
Answer by prateekagrawal(56)   (Show Source):
You can put this solution on YOUR website! f(x) = -4x^2 -8x +3
f(x) = -4(x^2 +2x) +3
f(x)= -4 (x^2 + 2x +1 -1) +3
f(x)= -4(x+1)^2 -4(-1) +3
f(x) = -4(x+1)^2 +4 +3
f(x) = -4(x+1)^2 +7
here (x+1)^2 is a whole square term... which will always be positive.
so, -4(x+1)^2 is always negative.
so, at x= -1 , f(x) =7 this is the maximum value of this...
second method:
f(x)= ax^2 +bx +c
if a>0 then minimum value
and if a<0 then maximum value.
and value is = f(-b/2a)
.
so, here a=-4 <0 so, maximum value....
.
and value is -(-8)/2(-4) = -1.
so,
f(-1) = -4(-1)^2 -8(-1)+3
f(-1) = -4+8+3
f(-1) = 7.
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