How could we find the slope of a parabola? Unlike a line, the steepness of a parabola varies, so we need to interpret the steepness of the curve at a point. For instance, look at ​x=2​ on the graph of ​f(x)=x2​ below.

What can we tell about the slope at that point? What if we utilize our knowledge of the slope of a straight line to estimate the slope at ​x=2​ by connecting it to a nearby point on the graph of ​f.

Here, we have come up with an estimate for the slope, but how can we improve our estimate?

How could we find the slope of a parabola? Unlike a line, the steepness of a parabola varies, so we need to interpret the steepness of the curve at a point. For instance, look at ​x=2​ on the graph of ​f(x)=x2​ below.

What can we tell about the slope at that point? What if we utilize our knowledge of the slope of a straight line to estimate the slope at ​x=2​ by connecting it to a nearby point on the graph of ​f.

Here, we have come up with an estimate for the slope, but how can we improve our estimate?