Show me the graph of x²+6x>_-5
Answer (1)
Start with the inequality:x² + 6x ≥ -5Move all terms to one side:x² + 6x + 5 ≥ 0Factorize:(x + 1)(x + 5) ≥ 0Critical points:x = -1 and x = -5Test ïntervals:For x < -5 → product is positive (✓)For -5 < x < -1 → product is negative (✗)For x > -1 → product is positive (✓)Solution set:x ≤ -5 or x ≥ -1Graph description:Parabola opening upward (U-shaped).Vertex at (-3, -4) which is above -5 on the y-axis.The shaded region is outside the interval (-5, -1), including the points x = -5 and x = -1.
