1* As seguintes funções são definidas em IR. Verifique quais são as funções quadráticas e identifique em cada uma os valores de a, b e c
A) F(x) = 2x (3x - 1) = 6x² - 2x
B) F(x) = (x + 2) (x - 2) - 4
C) F(x) = (1 + x) (1 - x) + x²
D) F(x) = (x+2)² - x (x + 1) = F(x)
2* Seja F(x) = 2x² - 3x + 1, calcule f( 
)
Soluções para a tarefa
Respondido por
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Bom dia Lucas!
Solução!
![A)\\\\\
2x(3x-1)=6 x^{2} -2x\\\\\
6 x^{2} -2x=6 x^{2} -2x\\\\\\
6 x^{2} -6 x^{2} -2x-2x=0\\\\\\
0=0~~N\~ao~~e\´~~uma~~func\~ao~~quadratica](https://tex.z-dn.net/?f=A%29%5C%5C%5C%5C%5C%0A2x%283x-1%29%3D6+x%5E%7B2%7D+-2x%5C%5C%5C%5C%5C%0A6+x%5E%7B2%7D+-2x%3D6+x%5E%7B2%7D+-2x%5C%5C%5C%5C%5C%5C%0A6+x%5E%7B2%7D+-6+x%5E%7B2%7D+-2x-2x%3D0%5C%5C%5C%5C%5C%5C%0A0%3D0%7E%7EN%5C%7Eao%7E%7Ee%5C%C2%B4%7E%7Euma%7E%7Efunc%5C%7Eao%7E%7Equadratica "A)\\\\\
2x(3x-1)=6 x^{2} -2x\\\\\
6 x^{2} -2x=6 x^{2} -2x\\\\\\
6 x^{2} -6 x^{2} -2x-2x=0\\\\\\
0=0~~N\~ao~~e\´~~uma~~func\~ao~~quadratica")
![B)\\\\\\\\\
(x+2).(x-2)=4\\\\\
x^{2} +2x-2x-4-4=0\\\\\
x^{2} -8=0\\\\\\\\\
E\´~~uma~~func\~ao~~quadratica\\\\\\\\
Coeficientes!~~a=1~~b=0~~c=-8](https://tex.z-dn.net/?f=B%29%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A%28x%2B2%29.%28x-2%29%3D4%5C%5C%5C%5C%5C%0A+x%5E%7B2%7D+%2B2x-2x-4-4%3D0%5C%5C%5C%5C%5C%0A+x%5E%7B2%7D+-8%3D0%5C%5C%5C%5C%5C%5C%5C%5C%5C%0AE%5C%C2%B4%7E%7Euma%7E%7Efunc%5C%7Eao%7E%7Equadratica%5C%5C%5C%5C%5C%5C%5C%5C%0A%0ACoeficientes%21%7E%7Ea%3D1%7E%7Eb%3D0%7E%7Ec%3D-8 "B)\\\\\\\\\
(x+2).(x-2)=4\\\\\
x^{2} +2x-2x-4-4=0\\\\\
x^{2} -8=0\\\\\\\\\
E\´~~uma~~func\~ao~~quadratica\\\\\\\\
Coeficientes!~~a=1~~b=0~~c=-8")
![D)\\\\\
(x+2)^{2}-x(x+1)=0\\\\\
x^{2} +4x+4- x^{2}-x=0\\\\\\
4x+4=0 \\\\\\
N\~ao~~e\´~~uma~~func\~ao~~quadratica!](https://tex.z-dn.net/?f=D%29%5C%5C%5C%5C%5C%0A%28x%2B2%29%5E%7B2%7D-x%28x%2B1%29%3D0%5C%5C%5C%5C%5C%0A+x%5E%7B2%7D+%2B4x%2B4-+x%5E%7B2%7D-x%3D0%5C%5C%5C%5C%5C%5C%0A4x%2B4%3D0+%5C%5C%5C%5C%5C%5C%0AN%5C%7Eao%7E%7Ee%5C%C2%B4%7E%7Euma%7E%7Efunc%5C%7Eao%7E%7Equadratica%21 "D)\\\\\
(x+2)^{2}-x(x+1)=0\\\\\
x^{2} +4x+4- x^{2}-x=0\\\\\\
4x+4=0 \\\\\\
N\~ao~~e\´~~uma~~func\~ao~~quadratica!")
![E)\\\\\\
f(x)=2 x^{2} +3x+1\\\\\\\\\
f\bigg( \dfrac{ \sqrt{ x^{2} } }{3}\bigg) =2 x^{2} +3x+1\\\\\\\\
f\bigg( \dfrac{ x }{3}\bigg)=2\bigg( \dfrac{ x }{3}\bigg)^{2}+3\bigg( \dfrac{ x }{3}\bigg)+1\\\\\\
f\bigg( \dfrac{ x }{3}\bigg)= \bigg(\dfrac{ 2 x^{2} }{9}\bigg)+\bigg( \dfrac{ 3x }{3}\bigg)+1\\\\\\
f\bigg( \dfrac{ x }{3}\bigg)= \dfrac{ 2 x^{2} }{9}+x+1\\\\\\](https://tex.z-dn.net/?f=E%29%5C%5C%5C%5C%5C%5C%0Af%28x%29%3D2+x%5E%7B2%7D+%2B3x%2B1%5C%5C%5C%5C%5C%5C%5C%5C%5C%0Af%5Cbigg%28+%5Cdfrac%7B+%5Csqrt%7B+x%5E%7B2%7D+%7D+%7D%7B3%7D%5Cbigg%29+%3D2+x%5E%7B2%7D+%2B3x%2B1%5C%5C%5C%5C%5C%5C%5C%5C%0Af%5Cbigg%28+%5Cdfrac%7B+x+%7D%7B3%7D%5Cbigg%29%3D2%5Cbigg%28+%5Cdfrac%7B+x+%7D%7B3%7D%5Cbigg%29%5E%7B2%7D%2B3%5Cbigg%28+%5Cdfrac%7B+x+%7D%7B3%7D%5Cbigg%29%2B1%5C%5C%5C%5C%5C%5C+%0A%0Af%5Cbigg%28+%5Cdfrac%7B+x+%7D%7B3%7D%5Cbigg%29%3D+%5Cbigg%28%5Cdfrac%7B+2+x%5E%7B2%7D++%7D%7B9%7D%5Cbigg%29%2B%5Cbigg%28+%5Cdfrac%7B+3x+%7D%7B3%7D%5Cbigg%29%2B1%5C%5C%5C%5C%5C%5C%0A%0Af%5Cbigg%28+%5Cdfrac%7B+x+%7D%7B3%7D%5Cbigg%29%3D+%5Cdfrac%7B+2+x%5E%7B2%7D++%7D%7B9%7D%2Bx%2B1%5C%5C%5C%5C%5C%5C+%0A%0A "E)\\\\\\
f(x)=2 x^{2} +3x+1\\\\\\\\\
f\bigg( \dfrac{ \sqrt{ x^{2} } }{3}\bigg) =2 x^{2} +3x+1\\\\\\\\
f\bigg( \dfrac{ x }{3}\bigg)=2\bigg( \dfrac{ x }{3}\bigg)^{2}+3\bigg( \dfrac{ x }{3}\bigg)+1\\\\\\
f\bigg( \dfrac{ x }{3}\bigg)= \bigg(\dfrac{ 2 x^{2} }{9}\bigg)+\bigg( \dfrac{ 3x }{3}\bigg)+1\\\\\\
f\bigg( \dfrac{ x }{3}\bigg)= \dfrac{ 2 x^{2} }{9}+x+1\\\\\\")
Bom dia!
Bons estudos!
Solução!
Bom dia!
Bons estudos!
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