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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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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 asSo 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
isSo 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
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