What is a Turn Point?
A Turn Point occurs at a vertex. This is a point where the graph changes directions. For example, the curve changes from increasing to decreasing or decreasing to increasing. The diagram will show more details on how a turn point works. Turn Points only provides general analysis of what the graph could look like. It does not, however, give any important information to solving or the actual shape of the curve. Calculus concepts, not discussed in this website, would provide a method for calculating the turn points without an actual graph.
Identifying a turn point is as easy as identifying the leading exponent and subtracting 1 from it. This will identify the number of possible turn points a polynomial can contain. For example, a quartic equation y=x^4 +x - 1 has a leading exponent of 4. Therefore, the number of possible turn points is 4-1=3. |
What is End Behavior? What does it tell us about a graph?
End Behavior provides a general understanding where the graph will progress towards, whether the end behavior is both going up/ down or one side goes up with the other side going down. This is determined from the leading (highest) exponent. If the leading exponent is even, then the graphs end behavior will go in the same direction, either up or down. If the leading exponent is odd, then the graphs end behavior will have one side going up and the other side going down.
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