Question

How can you graphically tell if a quadratic equation will have a complex solution?

Answer 1

if the equation doesn’t cross the X-axis

Answer 2

If it does not cross the x axis.

Explanation:

If the quadratic equation does not cross the x axis (or more specifically, if the quadratic is an upward opening parabola and the vertex is above the x axis, or if the quadratic is a downward opening parabola and the vertex is below the x axis), it will have no real solution

The fundamental theorem of algebra says that quadratics must have 2 solutions, so the solutions must be imaginary.