If you wanted the middle part of your roller coaster to have a steeper drop, would you use the graph of y = x3 – 2x2 + 6 or y = x3 – 4x2 + 6? Why? What part of the expression affected the steepness?

Using the same reasoning from part I, create an equation that will be steeper in the middle than both equations and explain your reasoning.

Question

If you wanted the middle part of your roller coaster to have a steeper drop, would you use the graph of y = x3 – 2x2 + 6 or y = x3 – 4x2 + 6? Why? What part of the expression affected the steepness?







Using the same reasoning from part I, create an equation that will be steeper in the middle than both equations and explain your reasoning.

imstuck · Answer

You would use the second equation to get a steeper drop on that.  While the function goes up as high as the first one (y=6), it drops significantly lower than does the first one.  The part of the expression that affected that was the -4x^2 part.

imstuck · Answer

An equation that would be steeper than both of those above could be x^3-6x^2+6

imstuck · Answer

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