Year 12s: what will be the first way you research your future options? >>

Absolute function

hi all, I need to sketch the graph of this eqn

|x^2 - 4|x| + 3|

How do i tackle this kind of qns?? thanks

OK, you'll have to bare with me on this one as I'm not 1005 sure how to do the whole questions yet...I'm still thinking about it as I right this...

...anyway....I'd do iot like this:

First consider the negative and positive values of x separately: you see that for both sets the graph will give the same answer. Thus if we call the function f(x) we see that f(x)=f(-x) and so all we now need to if draw one half the graph and 'reflect' it in the y-axis to get the other half. (And so if we now only consider the positive x-values we need only consider the function |x^2 -4x +3|).

Next consider where |x^2 -4x +3| crossed the y-axis. You should see this at (0,3). Then consider x^2- 4x +3 and sketch this graph for x>=0 (I'm assuming you know how too??? :smile:

)

You see this sketch has a part 'below' the x-axis, but is mostly 'above' the x-axis. The parts above are the part of the graph of |x^2 -4x +3|. Those below need 'flipping' to be above the x-axis, so reflect the part below the x-axix in the x-axis to make then above the x-axis.

You then have the graph of |x^2 -4|x| +3| for x>=0. You then reflect this in the y-axis to get the sketch graph for all x.

I hope this helps as I doubt I've explained it too well... :redface: