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Answer: {y∈R: y≤6} or [6,∞)
Explanation:
This problem doesn't require too much math. If you look at the equation given, you can see that it is a quadratic equation in the form of. Since this is a quadratic equation, we have an idea of that the graph would look like. It either curves up or down. Since this is a positive equation,
, we know that this is going to curve up. In order to find the minimum of the curve, you would use
.
This means the x value of the parabola is -2. To find the y, you plug -2 into the original equation.
Now that we know the y value of the minimum/vertex is 6, and it is determined that the parabola curves up, the range is y≤6 because the range starts at 6 and goes off toward infinity.