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.