a)
[tex]f(x)=-(x+2)^2-1\\\\f(x)=-(x^2+4x+4)-1\\\\f(x)=-x^2-4x-4-1\\\\f(x)=-x^2-4x-5\\\\a=-1, \ b=-4, \ c=-5\\\\\Delta=(-4)^2-4\cdot(-1)\cdot(-5)=16-20=\boxed{-4}[/tex]
b)
[tex]f(x)=\frac{1}{2}x^2-x\\\\a=\frac{1}{2}, \ b=-1, \ c=0\\\\\Delta=(-1)^2-4\cdot\frac{1}{2}\cdot0=1-0=\boxed1[/tex]
c)
[tex]f(x)=2x^2-3x-1\\\\a=2, \ b=-3, \ c=-1\\\\\Delta=(-3)^2-4\cdot2\cdot(-1)=9+8=\boxed{17}[/tex]
d)
[tex]f(x)=(2x+3)^2\\\\f(x)=4x^2+12x+9\\\\a=4, \ b=12, \ c=9\\\\\Delta=12^2-4\cdot4\cdot9=144-144=\boxed0[/tex]
e)
[tex]f(x)=(x-7)^2-9\\\\f(x)=x^2-14x+49-9\\\\f(x)=x^2-14x+40\\\\a=1, \ b=-14, \ c=40\\\\\Delta=(-14)^2-4\cdot1\cdot40=196-160=\boxed{36}[/tex]
Wykorzystane w zadaniu wzory
[tex](a+b)^2=a^2+2ab+b^2\\\\(a-b)^2=a^2-2ab+b^2\\\\y=ax^2+bx+c\\\\\Delta=b^2-4ac[/tex]
