SOLUTION: If y=X^2 +X - 12, what is the range of values for which Y > or = 0

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Question 889080: If y=X^2 +X - 12, what is the range of values for which Y > or = 0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First find when y=0
x%5E2%2Bx-12=0
%28x%2B4%29%28x-3%29=0
Two solutions:
x%2B4=0
x=-4
and
x-3=0
x=3
Now you have the number line broken into three distinct regions.
x%3C-4
-4%3Cx%3C3
x%3E3
Choose a value in each region and test the inequality.
x=-5
x%5E2%2Bx-12%3E=0
%28-5%29%5E2-5-12%3E=0
25-5-12%3E=0
8%3E=0
True
.
.
x=0
%280%29%5E2%2B0-12%3E=0
-12%3E=0
False
.
.
x=4
%284%29%5E2%2B4-12%3E=0
16%2B4-12%3E=0
8%3E=0
True
So the first and third regions are the solution regions and you include the endpoints since it is greater than or equal to.
.
.
(-infinity,-4]U[3,infinity)
.
.
.
graph%28300%2C300%2C-6%2C6%2C-6%2C6%2Cx%5E2%2Bx-12%29