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The Slope of a Parabola

What is the slope of y = x2?

Recall slope refers to the rate of change of a function. Begin by computing the slope between two points on the y = x2 function that are .001 units apart in the x-direction. Repeat the process for several (many) pairs of points. What happens to the slope? Organize your collection of data in a manner that may help a pattern stand out. Is there a pattern in your data that would help you predict the slope?


Investigate the slope of a different curve in the form y = xn and compare findings and generalizations among your classmates.

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