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2. Solve the following system of equations.
f(x) = 2x^2 – 5x– 7
g(x) = -4x^2+16
O (-1.2,17.88) and (-1.5, 17)
O (2.42,-7.4) and (-1.58, 5.9)
(-1.5, 17) and (3.7, 1788)
O (2.4,- 44) and (3.7, 17.88)

Respuesta :

2502272

Answer:

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Step-by-step explanation:i know

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Answer:

(2.42,-7.4) and (-1.58, 5.9)

Explanation:

  • f(x) = 2x² – 5x– 7
  • g(x) = -4x² + 16

Solve algebraically:

⇒ f(x) = g(x)

⇒ 2x² – 5x– 7 = -4x² + 16

⇒ 2x² - 5x - 7 + 4x² - 16 = 0

⇒ 6x² -5x -23 = 0

Now use the quadratic function:  [tex]\boxed{ \sf x = \dfrac{-b\pm\sqrt{b^2 - 4ac} }{2a}}[/tex]

Identify : a = 6, b = -5, c = -23

Solving Step Wise:

[tex]\rightarrow \sf x = \dfrac{-(-5)\pm\sqrt{(-5)^2 - 4(6)(-2)} }{2(6)} \ = \ \dfrac{5\pm\sqrt{577} }{12} \ = \ 2.42, -1.58[/tex]

Solve for y : 2(2.42)² - 5(2.42) -7  and  2(-1.58)² - 5(-1.58) - 7  = -7.4, 5.9

Coordinates: (2.42,-7.4) and (-1.58, 5.9)

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