Question

3. O vértice da função y=x²+2x-35 tem coordenadas:
(1 Ponto)

Answer 1

Explicação passo-a-passo:

Para calcular as coordenadas do vértice utilizamos as seguintes fórmulas:

$\boxed{x_{v} =\dfrac{-b}{2a}\ \ \ e\ \ \ y_{v}=\dfrac{-\Delta}{4a}}$

Temos a seguinte função:

$y=x^{2} +2x-35 \implies a=1,\ b=2,\ c=-35$

Calculando $x_{v}$:

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

Calculando $y_{v}$:

$y_{v}=\dfrac{-\Delta}{4a}\\\\y_{v}=\dfrac{-(b^{2}-4ac) }{4a}\\\\y_{v}=\dfrac{-(2^{2}-4.1.(-35)) }{4.1}\\\\y_{v}=\dfrac{-(4+140) }{4}\\\\y_{v}=\dfrac{-144 }{4}\\\\\boxed{y_{v}=-36}$

As coordenadas do vértice são:

$\boxed{\boxed{V(-1,-36)}}$