Question

Dany jest wzór funkcji kwadratowej f w postaci iloczynowej. podaj wzór funkcji f w postaci ogólnej, jeśli:

a) f(x)=-2/3(x+9)(x-1)

b) f(x)= 4/3x(x+6)

c)f(x)=1/2(x-4)do kwadratu

d) f(x)=5/6(x-2)(x+3)

e) f(x)=-1/4(x-4)(x+4)

f) f(x)= -1/2(x-2pierwiastki z 2)(x+3piewiastki z 2)

prosze o rozwiązanie, DAM NAJLEPSZE!!!!!!

Answer 1

a)

f(x) =(-2/3)*( x+9)( x - 1) = (-2/3)*( x^2 -x + 9x - 9) = (-2/3)(x^2 + 8x - 9)

f(x) = (-2/3) x^2 - (16/3) x + 6

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b)

f(x) = (4/3)x(x + 6) = (4/3)(x^2 + 6x) = (4/3) x^2 + 8 x

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c)

f(x) =(1/2)(x - 4)^2 = (1/2)( x^2 - 8x + 16) = (1/2) x^2 - 4 x + 8

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d)

f(x) = (5/6)(x - 2)( x + 3) = (5/6)*(x^2 +3x - 2x - 6 ) =

      =  (5/6) x^2  + (5/6) x - 5

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e)

f(x) =(- 1/4)(x-4)(x + 4) = (-1/4) ( x^2 - 16) = (-1/4) x^2 + 4

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f)

f(x) =(-1/2)(x - 2 p(2))(x + 3 p(2))

f(x) = (-1/2) ( x^2 + 3 p(2) x - 2 p(2) x - 12)

f(x) = (-1/2)( x^2 + p(2) x - 12)

f(x) = (- 1/2) x^2 - (1/2) p(2) x + 6

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