Question

1 - Determine as coordenadas (x,y) do vértice da parábola que representa a função Y=-x²+4x-3

Answer 1

$\large\boxed{\begin{array}{l}\sf y=-x^2+4x-3\\\sf\Delta=b^2-4ac\\\sf\Delta=4^2-4\cdot(-1)\cdot(-3)\\\sf\Delta=16-12\\\sf\Delta=4\\\sf x_V=-\dfrac{b}{2a}=-\dfrac{4}{2\cdot(-1)}=2\\\\\sf y_V=-\dfrac{\Delta}{4a}\\\\\sf y_V=-\dfrac{4}{4\cdot(-1)}=\dfrac{4}{4}=1\\\\\sf V(x_V,y_V)\\\sf V(2,1)\end{array}}$