Question

Demonstre a fórmula vértice:
V(-b/2.a ; -Δ/4.a)

Answer 1

$\mathsf{x_{V}=\dfrac{1}{2}(x_{1}+x_{2})}\\\mathsf{x_{V}=\dfrac{1}{2}(-\dfrac{b}{a})}\\\boxed{\boxed{\mathsf{x_{V}=-\dfrac{b}{2a}}}}$

$\mathsf{y_{V}=f(x_{V})}\\\mathsf{y_{V}=a.{(-\dfrac{b}{2a})}^{2}+b(-\dfrac{b}{2a})+c}$

$\mathsf{y_{V}=a\dfrac{{b}^{2}}{4{a}^{2}}-\dfrac{{b}^{2}}{2a}+c}\\\mathsf{y_{V} = \dfrac{{b}^{2}}{4a}-\dfrac{{b}^{2}}{2a}+c}\\\mathsf{y_{V} = \dfrac{{b}^{2}-2b^{2}+4ac}{4a}}$

$\mathsf{y_{V}=\dfrac{-b^{2}+4ac}{4a}}\\\mathsf{y_{V}=\dfrac{-1({b}^{2}-4ac)}{4a}}$

$\boxed{\boxed{\boxed{\mathsf{y_{V}=-\dfrac{\Delta}{4a}}}}}$