Q:

Nellie is analyzing a quadratic function f(x) and a linear function g(x). Will they intersect? f(x) g(x) graph of the function f of x equals one half times x squared, plus 2 x g(x) 1 5 2 10 3 15 (6 points) Yes, at positive x-coordinates Yes, at negative x-coordinates Yes, at negative and positive x-coordinates No, they will not intersect

Accepted Solution

A:
Hi! :)

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.