Slopes: Parallel and Perpendicular Lines

This is an introductory lesson for slopes of parallel and perpendicular lines. Knowledge about tangent lines is drawn on and refreshed.
Change the quadratic equation with the sliders. How does this affect the tangent line? Which line is parallel to the tangent line? Mathematically, how do we know this? How does the slope of the tangent line and the perpendicular line mathematically relate?