Nellie is analyzing a quadratic function f(x) and a linear function g(x). will they intersect?

For the answer to the question above, I think i've seen this question before.
If we substitute 13 to f(x) and get a value for x, then the two equations will intersect. So,
f(x) = x^2 + 6x +10
13 = x^2 + 6x+ 10
x^2 + 6x - 3 = 0

Solving the quadratic equations:
The roots of the equation is
x = 0.4641 and
x = -6.4541

Therefore, the line will intersect with the quadratic function.