Math CentralQuandaries & Queries


Question from Jalon, a student:

Hi, i am having trouble with my own math problem. if you could do it for me and show all working i would greatly appreciate it.

this is the problem:

The cubic function f(x) = (x+2)^3 touches the x axis only once at x = -2 (negative two). it could also be written as f(x) = (x+2)(x+2)(x+2)

Investigate the cubic functions below as well as the one above and comment clearly and fully on where they touch/intersect the x axis, and how these points relate to the given function.

a) f(x) = (x - 3)(x +4)(x - 2)
b) f(x) = x(x + 1)^2 (^2 = that means it squared)

Your comments should reference graphs illustrating your conclusions and display another 2 trinomial graphs that demonstrate your conclusions. particular attention should be given to the number of times your function crosses or touches the X axis.


We don't do all the work for you and send you the answer, but if you tell us where you are stuck, we'll point you in the right direction or solve a similar problem to show you how it is done.

Here's one piece of important information for this question: When a function touches the x-axis, that means that the value of the function f(x) = 0, so one of the factors (or more) must be zero. if f(x) = a(x) b(x) c(x)... then each unique value of x that makes at least one of the factors a zero must be a spot where the function crosses the axis.

Stephen at Math Central.

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