Answer: If k > 0 then the parabola won't touch x axis, and the discriminant will be less than 0.
Step-by-step explanation:
When x = h, what will y be? y will be equal to k. k is in other words, the lowest point (minimum) of the parabola, assuming p is positive.
The discriminant is less than zero if there are no real roots (ie the parabola doesn't touch the x axis at all).
The discriminant is greater than zero if there are 2 real roots (ie the parabola touches the x axis at two points).
The discriminant is equal to zero if there is one real root (ie the parabola touches the x axis at one point, with its vertex/lowest point).
SO:
If k = 0, the parabola's lowest point/vertex will be zero, and the discriminant will equal zero
If k > 0 then the parabola won't touch x axis, and the discriminant will be less than 0.
If k < 0 then the parabola will have two real roots that touch the x axis, and the discriminant will be greater than zero.
