Question

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

52 POINTS

Answer 1

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

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)