Question

encontre as coordenadas do vertice das função f(x)=2x²+8x-2
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Answer 1

Explicação passo-a-passo:

Para calcular as coordenadas do vértice de uma parábola, utilizamos as seguintes fórmula:

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

Temos que $f(x)=x^{2} +8x-2\implies a=2;b=8;c=-2$.

Calculando $x_{v}$:

$x_{v} =\dfrac{-b}{2a} \\\\x_{v} =\dfrac{-8}{2.2}\\\\x_{v} =\dfrac{-8}{4}\\\\\boxed{x_{v} =-2}$

Calculando $y_{v}$:

$y_{v} =\dfrac{-(b^{2}-4ac) }{4a}\\\\y_{v} =\dfrac{-(8^{2}-4.2.(-2)) }{4.2}\\\\y_{v} =\dfrac{-(64+16) }{8}\\\\y_{v} =\dfrac{-80 }{8}\\\\\boxed{y_{v}=-10}$

As coordenadas do vértice:

$\boxed{\boxed{C(-2,-10)}}$