Answer:
A quadratic function with imaginary roots will never intersect the x-axis, because imaginary numbers are not real numbers. Therefore, the graph of a quadratic function with imaginary roots will be a parabola that does not touch the x-axis.
Here is an example of a quadratic function with imaginary roots:
f(x) = x^2 + 2x + 5
The discriminant of this quadratic equation is b^2 - 4ac = 4^2 - 4 * 1 * 5 = -4. Because the discriminant is negative, the roots of the equation are imaginary.
The graph of this function is shown below: Attachment
As you can see, the graph does not intersect the x-axis. This is because the roots of the equation are imaginary, and imaginary numbers do not exist on the real number line.
x f(x)
-2 -1
-1 1
0 5
1 7
2 11