explain how the graph of gx is obtained from the graph of fx

explain how the graph of g(x) is obtained from the graph of f(x).

f(x)=x^2 g(x)= -3(x+2)^2 -5

Solution

f(x) = x^2 ;

g(x) = -3(x +2)^2 - 5 = -( 3(x+2)^2 +5 )

horizontal shift to left by 2 units : (x+2)^2

scaling vertically by 3 units : 3(x +2)^2

vertically shift by 5 units : 3(x +2)^2 + 5

Reflect about the x-axis : - 3(x +2)^2 - 5

g(x) = - 3(x +2)^2 - 5