for y=x^2(x-3)^3(2x+1) state the end behavior, determine the x and y intercepts and sketch a graph

Answer 1

Just think what the "x" would be if you multiplied x² and x³ and 2x together (the first terms of each factor). This will be the largest degree of the product polynomial. Of course it multiplies to 2x⁶ so that is the leading term in the resulting polynomial product.

Then use this key:

So this polynomial fits the upper left condition making the end behavior:

As x→∞, y→∞ and x→-∞, y→∞