a) x = 0 ∧ x = 2
[tex]y=4x^2-8x\\0=4x^2-8x\\4x^2-8x=0\\4x(x-2)=0\\\\4x=0\land x-2=0/+2\\\\x=0 \land x=2[/tex]
b) x = √5 ∧ x = -√5
[tex]y=20-4x^2\\0=20-4x^2/+4x^2\\4x^2=20/:4\\x^2=5/-5\\x^2-5=0\\(x-\sqrt{5} )(x+\sqrt{5} )=0\\\\x-\sqrt{5}=0\landx+\sqrt{5} =0\\\\x=\sqrt{5}=0\landx\land-\sqrt{5} =0[/tex]
c) x = 0 ∧ x = 24
[tex]y=\frac{1}{2} x^2+12x\\0=\frac{1}{2} x^2+12x/*2\\x^2+24x=0\\x(x+24)=0\\\\x=0\land x-24=0\\\\x=0\land x=24[/tex]
d) x = -5
[tex]y = { x }^{ 2 } +10x+25 \\0= { x }^{ 2 } +10x+25 \\0=(x+5)^2\\\\x+5=0\\\\x=-5[/tex]
e) funkcja nie ma miejsc zerowych
[tex]y = \dfrac{ 4 }{ 5 } { x }^{ 2 } +5 \\ 0 = \dfrac{ 4 }{ 5 } { x }^{ 2 } +5 /*5\\4x^2+25=0\\4x^2=-25\\x^2=-\frac{25}{4} \\\\x=\frac{5}{2}i\land x=-\frac{5}{2} i[/tex]
f) x = 1
[tex]y=-x^2+2x-1\\0=-x^2+2x-1/*(-1)\\0=x^2-2x+1\\(x-1)^2=0\\x-1=0\\x=1\\[/tex]
