Ryan Cross
05/01/2024 · Middle School
\( \left\{\begin{array}{l}\text { mostre que } \\ x v=\frac{-b}{2 a} \rightarrow x v=\frac{x 1+x 2}{2} \\ y v=\frac{-1}{4 a} \rightarrow y v=a x^{2} v+b x v+c\end{array}\right. \)
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Para mostrar as relações dadas, analisamos cada uma delas:
1. \( x_v = \frac{-b}{2a} \) implica \( x_v = \frac{x_1 + x_2}{2} \) porque a média das raízes de uma equação quadrática é igual à coordenada do vértice.
2. \( y_v = \frac{-1}{4a} \) implica \( y_v = a x_v^2 + b x_v + c \) porque substituindo \( x_v \) na função quadrática obtemos a coordenada \( y \) do vértice.
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