Odpowiedź:
z.8
a) f(x) = x² -2 x
p = [tex]\frac{-b}{2a} = \frac{2}{2*1} = 1[/tex]
q = f(p) = f(1) = 1² -2*1 = 1 - 2 = - 1
a =1
f(x) = a *(x - p)² + q - postać kanoniczna
Odp. f(x) = ( x - 1)² - 1
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b) f(x) = - x^2 +2 x + 8
a = - 1 b = 2 c = 8
p = [tex]\frac{-2}{2*(-1)} = 1[/tex]
q = f(p) = f(1) = - 1² +2*1 + 8 = - 1 + 2 + 8 = 9
f(x) = - ( x - 1)² + 9
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c) f(x) = [tex]\frac{1}{2} x^{2} + 3 x + \frac{1}{2}[/tex]
p = [tex]\frac{-3}{2*0,5}[/tex] = - 3
q = f(p) = f(-3) = 0,5*(-3)² + 3*(-3) + 0,5 = 0,5*9 - 9 + 0,5 = -4
f(x) = [tex]\frac{1}{2}[/tex] *( x + 3)² - 4
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z.9
a) f(x) = - 7 x² + 4 = - 7*( x - 0)² + 4
więc p = 0, q = 4 W = ( 0, 4)
b) f(x) = x² - 6 x + 5 = ( x - 3)² - 9 + 5 = ( x - 3)² - 4
W = ( 3, -4 )
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II sposób: p = [tex]\frac{6}{2*1} = 3[/tex]
q = f(3) = 3² -6*3 + 5 = 9 - 18 + 5 = - 9 +5 = - 4
a = 1
f(x) = ( x - 3)² - 4
W = ( p, q ) = ( 3, - 4)
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c) f(x) = [tex]\frac{1}{2} x^{2} + 2 x - 3[/tex]
p = [tex]\frac{-b}{2 a} = \frac{-2}{2*0,5} = -2\\[/tex]
q = f(p) = f( -2) = 0,5*(-2)² + 2*(-2) - 3 = 0,5*4 - 4 - 3 = 2 - 4 - 3 = -5
W = ( -2, - 5)
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Szczegółowe wyjaśnienie:
