Part 4/6:
Degree 1 (Linear): The graph is a straight line. For example, ( y = mx + b ) will always yield a linear function.
Degree 2 (Quadratic): The graph will form a parabola. Depending on the coefficients, it may open upwards (if ( a_2 > 0 )) or downwards (if ( a_2 < 0 )).
Degree 3 (Cubic): This graph can exhibit up to three directional shifts, effectively made of two curves joined at a point of inflection.
Higher Degrees: As the degree increases, the complexity of the graph increases as well. For example, a fourth-degree polynomial typically reflects a 'w' shape or 'm' shape depending on its coefficients, whereas odd-degree polynomials typically continue to exit from opposite sides.