Math CentralQuandaries & Queries


Question from kelsey:

find the coordinates of the vertex f(x)= l3x-6l + 1

Hi Kelsey,

I can help get you started. The key to this is to examine the graph of f(x) = |x|.

If x ≥ 0 then |x| = x so for x ≥ 0 f(x) = |x| = x.
If x < 0 then |x| = -x so for x < 0 f(x) = |x| = -x.

Thus the graph of f(x) = |x| is

f(x) = |x|
f(x) = |x|

Now what about g(x) = |x| + 1. For each x the value of g(x) is one more than the value of f(x). Thus the graph of g(x) is

g(x) = |x| + 1
g(x) = |x| + 1

So the vertex appears where the variable expression inside the absolute value signs is zero.

I hope this helps,

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