Mathematics

# L is a quadratic function whose graph is a parabola opening upward and has a vertex on the y-axis. The graph of the new function t defined by t(y) = 2 - L(y - 5) has a range defined by the interval

$L(x)=ax^2+b\ \ \ and\ \ \ a>0\ \ \ \Rightarrow\ \ \ the\ Vertex=(0;\ b)\\\\t(x)=2-L(x-5)=2-[a(x-5)^2+b]=2-a(x-5)^2-b=\\.\ \ \ \ =-a(x-5)^2+(2-b)\\\\\ \ \ \Rightarrow\ \ the\ Vertex=(5;\ 2-b) \\\\the\ graph\ is\ a \ parabola\ downward$