Question

How do you solve and graph `x² + 2x - 15 ≤ 0`?

Answer 1

Closed interval [-5, 3]

Explanation:

y = x^2 + 2x - 15 <= 0 (1)
First, solve the quadratic equation y = 0 to find the 2 x-intercepts.
Find 2 real roots that have as sum (-b = -2) and as product (-15). They are 3 and -5.
Since a > 0, the parabola opens upward. Between the 2 x-intercepts, the parabola is below the x-axis, meaning f(x) < 0.
The solution set is the closed interval [-5, 3].
The 2 end points -5 and 3 are included in the solution set.
graph{x^2 + 2x - 15 [-40, 40, -20, 20]}