Question

Qual a coordenada do vértice da função?​

Answer 1

Explicação passo-a-passo:

Para calcular as coordenadas do vértice, utilizamos as seguintes fórmulas:

$x_{v} =\dfrac{-b}{2a}$

$y_{v}=\dfrac{-\Delta}{4a}=\dfrac{-(b^{2}-4ac) }{4a}$

Temos que $y=x^{2} -2x-3\implies a=1;b=-2;c=-3$.

Calculando $x_{v}$:

$x_{v} =\dfrac{-b}{2a}\\\\x_{v} =\dfrac{-(-2)}{2.1}\\\\x_{v} =\dfrac{2}{2}\\\\\boxed{x_{v} =1}$

Calculando $y_{v}$:

$y_{v}=\dfrac{-(b^{2}-4ac) }{4a}\\\\y_{v}=\dfrac{-((-2)^{2}-4.1.(-3)) }{4.1}\\\\y_{v}=\dfrac{-(4+12) }{4}\\\\y_{v}=\dfrac{-16 }{4}\\\\\boxed{y_{v}=-4}$

$\boxed{\boxed{V(1,-4)}}$