In complete sentences, explain why 1/(x^2+2x+9) <0 has no solution. Do NOT solve the inequality.

Answer 1

for 1/y < 0 , y has to be negative

so look at the graph of y = x^2 + 2x + 9
the x of its vertex is -b/2a = -2/2 = -1, and
the y of the vertex is (-1)^2 - 2 + 9 = 8
the vertex is (-1,8), which lies above the x-axis
and of course our parabola opens upwards, so it cannot go below the x-axis