range of values for m?

[hadimotamedi]

Dear All
For what values of m, the following curve will pass from all of the four quadrants of the xy-plane?
y=(m+2)x^2-2x+1

[blitzer6266]

Hint: A parabola will hit all quadrants iff it has a positive and negative root (picture is a good enough proof)

This should lead you to the right answer

[DDswife]

Hint 2: a quadratic equation whose leading coefficient doesn't necessarily have to be one. The first coefficient might be 0. In this case, it won't be in the 4 quadrants

To check of the roots have different signs, their product should be negative. And the products of the roots of ax^2+bx+c = 0 is c/a

[DDswife]

Hint 3. y(0) =1. So, it will only have a positive and a negative zeros if the leading coefficient is negative