Math CentralQuandaries & Queries


Question from Bruce, a student:

The equation is x2-12.

I need to find the x-y intercepts and horizontal intervals (increasing & decreasing)

I would have thought the y intercept would be (0,-12) however the book came up with something different.

Hi Bruce,

The y intercepts of y = x2 - 12 are the points where the graph crosses the y-axis. Since points on the y-axis are precisely the points that have their x-coordinates equal to zero you can find the y-intercepts by substituting x = 0 and solving for y. Thus

y = 02 - 12 = -12

Thus I agree with you, there is one y-intercept at (0, -12).

Likewise the x-intercepts are obtained by substituting y = 0. In this case

0 = x2 - 12 so x = ±√12


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