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State the intervals for which the given quadratic is positive and when it is negative.
Give answer in interval notation.
y=-2x^2-14+36

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mhanifa

Answer:

  • Positive at (-9, 2)
  • Negative at ( -oo, -9) or (2, + oo)

Step-by-step explanation:

Given function

  • y= -2x^2 - 14x + 36

Getting zero's

  • -2x^2 - 14x + 36 = 0
  • x^2 + 7x - 18 = 0
  • x = ( -7 ± √(49 +72))/2 = ( -7 ± 11)/2
  • x = - 9 and x = 2

As the x^2 has negative coefficient, the function is positive between -9 and 2

  • - 9 < x < 2 or
  • (-9, 2)

And it is negative at:

  • x < -9 and
  • x > 2
  • or
  • ( -oo, -9) or (2, + oo)

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