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wzór
y=a(x-x_1)(x-x_2)
a)
y=x^2-x-6, -x=2x-3x
y=x^2-2x+3x-6
y=x(x-2)+3(x-2)
y=(x-2)(x+3)
b)
y=-x^2+x+6
y=-(x^2-x-6) , -x=2x-3x
y=-(x^2+2x-3x-6)
y=-[x(x+2)-3(x+2)]
y=-(x+2)(x-3)
c)
y=2x^2-3x-2 , -3x=-4x+x
y=2x^2-4x+x-2
y=2x(x-2)+(x-2)
y=(x-2)(2x+1) \\ y=2(x-2)(x+\frac{1}{2})
d)
y=-2x^2+4x-1
a=-2 , b=4, c=-1
\Delta=b^2-4ac=16-4 \cdot (-2) \cdot (-1)=8
\sqrt\Delta=\sqrt{4 \cdot 2}=2\sqrt2
x_1=\frac{-b-\sqrt\Delta}{2a}=\frac{-4-2\sqrt2}{2 \cdot (-2)}=\frac{-\not2^1(2+\sqrt2)}{2\cdot (-\not2^1)}=\frac{2+\sqrt2}{2}
x_2=\frac{-b+\sqrt\Delta}{2a}=\frac{-4+2\sqrt2}{2 \cdot (-2)}=\frac{-\not2^1(\sqrt2-2)}{2\cdot (-\not2^1)}=\frac{\sqrt2-2}{2}
y=-2(x-\frac{2+\sqrt2}{2})(x-\frac{\sqrt2-2}{2})
e)
y=3x^2-7x+4 , -7x=-3x-4x
y=3x^2-3x-4x+4
y=3x(x-1)-4(x-1)
y=(x-1)(3x-4)
y=3(x-1)(x-\frac{4}{3})