Quadratic functions

Question

What is the range of the relation defined by y-5=-1/4(x+2)^2?

Answer 1

The vertex of the parabola is found by putting the equation in vertex form which is: f(x) = a(x-h)^2 + k.   So the vertex is (h,k) in this example (-2,5).  Since a=-1/4 the negative value means it opens downward.  So the y value of the vertex is the highest point on the range which is 5.  The lowest point is infinity since it goes down - forever.  So the range is (5,-∞).