Question

calcule x para que a função tenha um mínimo:
a) y= 3x²-4x+1
b) y= x²+12x+11

Answer 1

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$\large\begin{array}{l} \textsf{Calcular x para que as fun\c{c}\~oes quadr\'aticas assumam seu}\\\textsf{valor m\'inimo (o x do v\'ertice).}\\\\\\ \mathsf{a)~y=3x^2-4x+1}\quad\Rightarrow\quad\left\{\! \begin{array}{l} \mathsf{a=3}\\\mathsf{b=-4}\\\mathsf{c=1} \end{array} \right. \end{array}$


$\large\begin{array}{l} \textsf{Como }\mathsf{a=3>0}\textsf{ (positivo), a fun\c{c}\~ao assume um valor m\'inimo em}\\\\ \mathsf{x=x_v=-\,\dfrac{b}{2a}}\\\\ \mathsf{x=-\,\dfrac{(-4)}{2\cdot 3}}\\\\ \mathsf{x=\dfrac{4}{2\cdot 3}}\\\\ \mathsf{x=\dfrac{\diagup\!\!\!\! 2\cdot 2}{\diagup\!\!\!\! 2\cdot 3}}\\\\ \boxed{\begin{array}{c}\mathsf{x=\dfrac{2}{3}}\end{array}}\qquad\quad\checkmark \end{array}$


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$\large\begin{array}{l} \mathsf{b)~y=x^2+12x+11}\quad\Rightarrow\quad\left\{\! \begin{array}{l} \mathsf{a=1}\\\mathsf{b=12}\\\mathsf{c=11} \end{array} \right. \end{array}$


$\large\begin{array}{l} \textsf{Como }\mathsf{a=1>0}\textsf{ (positivo), a fun\c{c}\~ao assume um valor m\'inimo em}\\\\ \mathsf{x=x_v=-\,\dfrac{b}{2a}}\\\\ \mathsf{x=-\,\dfrac{12}{2\cdot 1}}\\\\ \mathsf{x=-\,\dfrac{12}{2}}\\\\ \boxed{\begin{array}{c}\mathsf{x=-6} \end{array}}\qquad\quad\checkmark \end{array}$

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$\large\begin{array}{l} \textsf{D\'uvidas? Comente.}\\\\\\ \textsf{Bons estudos! :-)} \end{array}$


Tags: função quadrática segundo grau vértice mínimo álgebra