SOLUTION: Solve the inequality and express the solution in interval notation: x^2 - 6x + 11 <18

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Question 38734: Solve the inequality and express the solution in interval notation:
x^2 - 6x + 11 <18
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
For +x%5E2+-+6x+%2B+11+%3C+18+, first we solve +x%5E2+-+6x+%2B+11+=+18+

+x%5E2+-+6x+-+7+=+0+ --> which will help us to find the solution to +x%5E2+-+6x+-+7+%3C+0+

--> (x-7)(x+1) = 0
so either x-7=0 or x+1=0
so x=7 or x=-1

From my knowldege of quadratics, i know that a x%5E2 function is u-shaped and that a -x%5E2 function is n-shaped.

So we know that the curve is u-shaped and that it crosses the x-axis at x=-1 and x=7. So, we want it where the curve is LESS THAN zero... this is between these 2 values.

So answer is -1 < x < 7

jon.