SOLUTION: What is the solution of the system of inequalities?
y≥ x^2+2x+2
y< -x^2-4x-2
Thank You!
Algebra.Com
Question 695832: What is the solution of the system of inequalities?
y≥ x^2+2x+2
y< -x^2-4x-2
Thank You!
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
First let's look at the graph of the two parabolas:
The red one is and the green one is . The solution to would be the red parabola and all the area above/inside the bowl. The solution to would be all the area below/inside the green parabola. (Not the green parabola itself because that is where y equals and the inequality does not include "or equal to".)
So the solution to the system is where these two areas overlap each other: The enclosed area between the two parabolas. To express this solution we must first find the two points where the parabolas intersect. Setting
and solving for x we should be able to find the points of intersection. Subtracting the entire right side we get:
Factor out the GCF of 2:
Factoring the trinomial:
From the Zero Product Property:
x + 1 = 0 or x + 2 = 0
Solving:
x = -1 or x = -2
Using these x values and either equation for the parabola we can find that the y values for each x are 1 and 2, respectively. So the points of intersection are:
(-1, 1) and (-2, 2)
So the x values of the solution are between -1 and -2, inclusive:
and the y values of the solution are:
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