How do you determine where and if a quadratic function and and linear function intercept?

To determine where a quadratic function and a linear function intercept, set their equations equal to each other and solve for the variable. This will typically result in a quadratic equation, which can be solved using factoring, completing the square, or the quadratic formula. The solutions will provide the x-coordinates of the points of intersection, and substituting these x-values back into either function will give the corresponding y-coordinates. If there are no real solutions, the functions do not intersect.