Hello, Tom G!
Find the range of values that can take
if is positive for all real .
The function is an up-opening parabola.
Its vertex is at: .
. . and:
Hence, its vertex (lowest point) is: .
If the parabola is to be above the x-axis, then: .
There are two cases:
. . .But this gives us: . and . . . impossible
. . .which gives us: . and
Therefore, the range is: .