Question

determine o vertice do grafico da funçao x2 -4×-3

Answer 1

$x^2-4x-3=0\\\\\\ x_v= \dfrac{-b}{2a} \to~~ x_v= \dfrac{-(-4)}{2.1} \to~~ x_v= \dfrac{4}{2} \to~~ \boxed{x_v=2}\\\\\\\\ y_v= \dfrac{-\Delta}{4a} \to~~ \\\\\\\Delta=b^2-4ac\to \Delta=(-4)^2-4.1.(-3)\to \Delta=16+12\to \underline{~\Delta=28~} \\\\\\ y_v= \dfrac{-28}{4.1} \to~~ y_v= \dfrac{-28}{4} \to~~ \boxed{y_v=-7}\\\\\\\\\\ \large\boxed{\boxed{S=\{2~;~-7\}}}$

Answer 2

Função: f(x) = x² - 4x - 3
Temos: a = 1, b = - 4 e c = - 3

Fórmula do x do vértice:
x= - b/2a
x= - (- 4)/2.1
x= 4/2
x= 2

Fórmula do y do vértice:
y= - Delta/4a

Sendo Delta = b² - 4ac, temos:
Delta = (-4)² - 4.1.(-3)
Delta = 16 + 12
Delta = 28

y= - 28/4.1
y= - 28/4
y= - 7

As coordenadas do vértice são: (2,-7)