Question

Identify the intervals on which each quadratic function is positive Part 1

1. y = x^2 + 9x + 18
2. y = x^2 + 2x - 8
3. y = x^2 - 5x - 24

Answer 1

Answer: 1) (-∞, -6) U (-3, ∞)

2) (-∞, -4) U (2, ∞)

3) (-∞, -3) U (8, ∞)

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, ∞)