y= a(x-p)²+q p= -b/2a q= -Δ/4a W (p,q)
1)
f(x)=x²-4x+1
p= 4/2 = 2
Δ=16-4=12
q= -12/4 = -3
f(x) = (x-2)²-3
W (2,-3)
Zb. wart. <-3, +∞)
df/dx = 2x-4
2x-4=0
x=2
f maleje (-∞ ;2)
f rosnie (2; +∞)
2)
f(x)=-x²-6x-6
p= 6/-2 = -3
Δ=36-24=12
q= -12/-4 = 3
f(x) = -(x+3)²+3
W (-3,3)
Zb. wart. (-∞ ; 3>
df/dx = -2x-6
-2x-6=0
x=-3
f rosnie (-∞ ;-3)
f maleje (-3; +∞)
3)
f(x)=-0,5x²+x
p= -1/-1 = 1
Δ=1
q= -1/-2 = 1/2
f(x) = -0,5(x-1)²+ 1/2
W (1;1/2)
Zb. wart. (-∞; 1/2>
df/dx = -x+1
-x+1=0
x=1
f rosnie (-∞ ;1)
f maleje (1; +∞)
