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[tex]y=Ax^2+Bx+C[/tex]. 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, [tex](+3x^2)[/tex], we know that this is going to curve up. In order to find the minimum of the curve, you would use [tex]\frac{-b}{2a}[/tex].
[tex]\frac{-12}{2(3)}=-2[/tex]
This means the x value of the parabola is -2. To find the y, you plug -2 into the original equation.
[tex]f(2)=3(-2)^2+12(-2)+18[/tex]
[tex]f(2)=6[/tex]
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.
