Question

04) Calcule as coordenadas do vértice da seguinte função y = 4x2 – 16x + 7.

( ) V = (– 3, – 9)

( ) V = (3, – 9)

( ) V = (2, – 9)

( ) V = (2, 9)

( ) V = (– 2, – 9)​

Answer 1

Explicação passo-a-passo:

Xv = -b/2a = -(-16)/2.4 = 16/8 = 2

Yv = 4.2² - 16.2 + 7 = 4.4 - 32 + 7 = 16 - 32 + 7 = -9

V = (2, -9)

Answer 2

Fórmula Para Encontrar o Vértice:

$\boxed{\begin{array}{lr} \boxed{\begin{array}{lr} \\ \large \sf \: x_{v} = \dfrac{ - b}{2.a} \\ \ \\ \large \sf \: y_{v} = \dfrac{ - \Delta}{4.a} \\ \: \end{array}} \end{array}}$

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• Cálculo Discriminante:

$\boxed{\begin{array}{lr} \\ \large \sf \Delta = {b}^{2} - 4ac \\ \\ \large \sf \Delta = { (- 16)}^{2} - 4 \cdot4 \cdot7 \\ \\ \large \sf \Delta = 256 - 112 \\ \\ \boxed{ \red{\large \sf\Delta = 114}} \\ \: \end{array}}$

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• Vértice:

$\large \sf \: x_{v} = \dfrac{16}{8} = \boxed{ \red{ \large \sf 2}} \\ \\ \\ \large \sf \: y_{v} = \dfrac{ - 144}{16} = \boxed{ \red{ \large \sf - 9}}$

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➡️ Resposta:

• V = ( 2, -9 )