This problem is about being able to sketch a graph with the given polynomial. By factoring the equation and setting the factors equal to 0 to solve for zeroes, we can find our points in order to graph it. Besides finding out our x-intercepts and y-intercepts, we also need to know our end behaviors (how the graph acts at the extremes). We can identify the end behavior by examining our leading coefficient (whether it's positive or negative) and the degree (whether it's even or negative). There are four types of end behaviors (even positive, even negative, odd positive, and odd negative). Not only do you need to know the end behaviors but also the zero's multiplicity so you know how it acts around the x-axis, this is where TBC-123 comes in handy. To accurately sketch the graph, we can also find our extremas, the minimum and maximum, and the intervals of increase and decrease.
To make sure you're doing all this accurately, you should pay special attention to your factors and end behaviors. If you can't factor your equation correctly, then your zeros will come out different and not precise. Also, the end behaviors must be the correct so make sure you have the song and dance moves memorized so you know how the graph will look like! Lastly, you should make sure you have the TBC-123 down. If there's a M of 1, that means the graph will go THROUGH the point. If the M is 2, then the graph will BOUNCE off the point. Then if your M is 3, your graph will curve through the point. Remember that each point is a door and it's the only way you can get through the x-axis. If there isn't a point (door) there, that means it's just a wall and you can't walk through a wall!
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