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

##### 1 Answer

Apr 6, 2016

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]}