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#1 2009-07-05 18:14:33

Shwvvn
Member
Registered: 2009-07-05
Posts: 2

Modulus Function Question

Sketch the graph of y = |x^2 -5x + 4|. If the solutions of |x^2 -5x + 4| < 2 are 5/2 - 1/2sqroot 16 < x < 2 and a < x < b, use the graph to deduce the values of a and b.

How do I find the values of a and b?

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#2 2009-07-05 21:00:23

Identity
Member
Registered: 2007-04-18
Posts: 934

Re: Modulus Function Question

To solve an inequality like that, one way is to graph

and
and find where the first graph is below the second graph.

can be written as

So the turning point is at

.

However, due to the modulus sign, we must reflect every negative y-value about the x-axis, so the turning point of

is

So when you sketch the graph it should look like a normal parabola except the part between the x-intercepts has been reflected about the x-axis. This graph should cross the line y=2 at 4 points, and if you graph you will see there are two sections below the line y = 2.

To find the intercept between the two graphs,

So for

and

,

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