Answer: 1) (-∞, -6) U (-3, ∞)
2) (-∞, -4) U (2, ∞)
3) (-∞, -3) U (8, ∞)
Step-by-step explanation:
Find the zeros. Since the a-value is positive, the curve will be positive to the left of the leftmost zero and to the right of the rightmost zero. + - +
←---|----|--→
1) y = x² + 9x + 18
y = (x + 3)(x + 6)
0 = (x + 3)(x + 6)
0 = x + 3 0 = x + 6 + -- +
x = -3 x = -6 ←------|-----------|--------→
-6 -3
Positive Interval: (-∞, -6) U (-3, ∞)
2) y = x² + 2x - 8
y = (x + 4)(x - 2)
0 = (x + 4)(x - 2)
0 = x + 4 0 = x - 2 + -- +
x = -4 x = 2 ←------|-----------|--------→
-4 2
Positive Interval: (-∞, -4) U (2, ∞)
3) y = x² - 5x - 24
y = (x + 3)(x - 8)
0 = (x + 3)(x - 8)
0 = x + 3 0 = x - 8 + -- +
x = -3 x = 8 ←------|-----------|--------→
-3 8
Positive Interval: (-∞, -3) U (8, ∞)
