Session 5 - Quadratic Curve and Line

When we consider a quadratic function and a linear function together, we can have 0, 1, or 2 points of intersection. each point of intersection satisfies both the quadratic function and the linear function.

Therefore, each point of intersection corresponds to a solution of the quadratic equation formed by equating the quadratic function in the y=f(x) form to the linear function in the y=mx+c form. This corresponds to how two linear equations of the form y = m_1x + c_1 and y = m_2x + c_2 can have 0, 1, or infinitely many points of intersection and can be solved by equating the two linear functions to form a linear equation.

The number of points of intersection between a quadratic curve and a line can be determined by the discriminant of the corresponding quadratic equation.