Dada a função y = x² - 6x + (3m – 2), calcule m de modo que o valor
mínimo da função seja – 8.
a) m = 2.
b) m = -3.
c) m = 1.
d) m = - 4.
Respostas
respondido por:
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Boa noite Thais!
Solução!
veja que -8 é o valor de m que é igual a y no ponto minimo imposto no problema.
![y= x^{2} -6x+(3m-2)\\\\\\
-8= x^{2} -6x+(3m-2)\\\\\
0= x^{2} -6x+(3m-2)+8\\\\\
0= x^{2} -6x+(3m-2+8)\\\\\\
0= x^{2} -6x+3m+6](https://tex.z-dn.net/?f=y%3D+x%5E%7B2%7D+-6x%2B%283m-2%29%5C%5C%5C%5C%5C%5C%0A-8%3D+x%5E%7B2%7D+-6x%2B%283m-2%29%5C%5C%5C%5C%5C%0A0%3D+x%5E%7B2%7D+-6x%2B%283m-2%29%2B8%5C%5C%5C%5C%5C%0A0%3D+x%5E%7B2%7D+-6x%2B%283m-2%2B8%29%5C%5C%5C%5C%5C%5C%0A0%3D+x%5E%7B2%7D+-6x%2B3m%2B6 "y= x^{2} -6x+(3m-2)\\\\\\
-8= x^{2} -6x+(3m-2)\\\\\
0= x^{2} -6x+(3m-2)+8\\\\\
0= x^{2} -6x+(3m-2+8)\\\\\\
0= x^{2} -6x+3m+6")
![y=\Delta\\\\\\
a=1\\\\\
b=-6\\\\\
c=(3m+6)\\\\\\\](https://tex.z-dn.net/?f=y%3D%5CDelta%5C%5C%5C%5C%5C%5C%0Aa%3D1%5C%5C%5C%5C%5C%0Ab%3D-6%5C%5C%5C%5C%5C%0Ac%3D%283m%2B6%29%5C%5C%5C%5C%5C%5C%5C+ "y=\Delta\\\\\\
a=1\\\\\
b=-6\\\\\
c=(3m+6)\\\\\\\")
![b^{2} -4.a.c=0\\\\\\
(-6)^{2}-4.1.(3m+6)=0\\\\\\
36-12m-24=0\\\\\\
-12m+12=0\\\\\\
-12m=-12\\\\\
m= \dfrac{-12}{-12}\\\\\\
m=1](https://tex.z-dn.net/?f=b%5E%7B2%7D+-4.a.c%3D0%5C%5C%5C%5C%5C%5C%0A%28-6%29%5E%7B2%7D-4.1.%283m%2B6%29%3D0%5C%5C%5C%5C%5C%5C%0A36-12m-24%3D0%5C%5C%5C%5C%5C%5C%0A-12m%2B12%3D0%5C%5C%5C%5C%5C%5C%0A-12m%3D-12%5C%5C%5C%5C%5C%0Am%3D+%5Cdfrac%7B-12%7D%7B-12%7D%5C%5C%5C%5C%5C%5C%0Am%3D1%0A%0A%0A%0A+ "b^{2} -4.a.c=0\\\\\\
(-6)^{2}-4.1.(3m+6)=0\\\\\\
36-12m-24=0\\\\\\
-12m+12=0\\\\\\
-12m=-12\\\\\
m= \dfrac{-12}{-12}\\\\\\
m=1")
Boa noite!
Bons estudos!
Solução!
veja que -8 é o valor de m que é igual a y no ponto minimo imposto no problema.
Boa noite!
Bons estudos!
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