Odpowiedź:
- 6, 4 A = ( 0, - 6 )
y = a*( [tex]x - x_1 )*( x - x_2) = a*( x + 6)*( x - 4)[/tex]
A = ( 0, - 6 ) więc po podstawieniu mamy
- 6 = a*( 0 + 6)*(0 - 4)
- 6 = a*6*( - 4) = - 24 a / : ( - 24)
a = [tex]\frac{- 6}{- 24} = \frac{1}{4}[/tex]
więc
y = [tex]\frac{1}{4} *(x + 6)*( x - 4)[/tex] - postać iloczynowa
---------------------------------
y = [tex]\frac{1}{4} *(x^{2} - 4 x + 6 x - 24 ) = \frac{1}{4} *(x^{2} +2 x - 24 ) = \frac{1}{4}x^{2} + \frac{1}{2} x - 6[/tex]
y = [tex]\frac{1}{4} x^{2} + \frac{1}{2} x - 6[/tex] - postać ogólna
----------------------
II sposób:
y = a [tex]x^{2} + b x + c[/tex]
0 = a*(-6)² - 6 b + c
0 = a*4² + 4 b + c
- 6 = a*0^2 + 0*b + c ⇒ c = - 6
c = - 6
-----------
zatem po podstawieniu - 6 za c mamy
36 a - 6 b - 6 = 0 / : 6
16 a + 4 b - 6 = 0 / : 2
czyli
6 a - b - 1 = 0 ⇒ b = 6 a - 1
8 a + 2 b - 3 = 0
8 a + 2*(6 a - 1) - 3 = 0
8 a + 12 a - 2 - 3 = 0
20 a = 5 / : 20
a = [tex]\frac{1}{4}[/tex]
-------
b = 6*[tex]\frac{1}{4} - 1 = \frac{6}{4} - \frac{4}{4} = \frac{2}{4} = \frac{1}{2}[/tex]
---------------------------------------------
Mamy: a = [tex]\frac{1}{4} ,[/tex] b = [tex]\frac{1}{2}[/tex] , c = - 6
zatem
Odp. y = [tex]\frac{1}{4} x^{2} + \frac{1}{2} x - 6[/tex]
========================
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Odpowiedź:
- 6, 4 A = ( 0, - 6 )
y = a*( [tex]x - x_1 )*( x - x_2) = a*( x + 6)*( x - 4)[/tex]
A = ( 0, - 6 ) więc po podstawieniu mamy
- 6 = a*( 0 + 6)*(0 - 4)
- 6 = a*6*( - 4) = - 24 a / : ( - 24)
a = [tex]\frac{- 6}{- 24} = \frac{1}{4}[/tex]
więc
y = [tex]\frac{1}{4} *(x + 6)*( x - 4)[/tex] - postać iloczynowa
---------------------------------
y = [tex]\frac{1}{4} *(x^{2} - 4 x + 6 x - 24 ) = \frac{1}{4} *(x^{2} +2 x - 24 ) = \frac{1}{4}x^{2} + \frac{1}{2} x - 6[/tex]
y = [tex]\frac{1}{4} x^{2} + \frac{1}{2} x - 6[/tex] - postać ogólna
----------------------
II sposób:
y = a [tex]x^{2} + b x + c[/tex]
0 = a*(-6)² - 6 b + c
0 = a*4² + 4 b + c
- 6 = a*0^2 + 0*b + c ⇒ c = - 6
c = - 6
-----------
zatem po podstawieniu - 6 za c mamy
36 a - 6 b - 6 = 0 / : 6
16 a + 4 b - 6 = 0 / : 2
czyli
6 a - b - 1 = 0 ⇒ b = 6 a - 1
8 a + 2 b - 3 = 0
8 a + 2*(6 a - 1) - 3 = 0
8 a + 12 a - 2 - 3 = 0
20 a = 5 / : 20
a = [tex]\frac{1}{4}[/tex]
-------
b = 6*[tex]\frac{1}{4} - 1 = \frac{6}{4} - \frac{4}{4} = \frac{2}{4} = \frac{1}{2}[/tex]
---------------------------------------------
Mamy: a = [tex]\frac{1}{4} ,[/tex] b = [tex]\frac{1}{2}[/tex] , c = - 6
zatem
Odp. y = [tex]\frac{1}{4} x^{2} + \frac{1}{2} x - 6[/tex]
========================
Szczegółowe wyjaśnienie: