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:

and

. . .But this gives us: .and. . . impossible

and

. . .which gives us: . and

Therefore, the range is: .