Question 933049
{{{f (x) = (x^2-2x + 1)/20}}} 

"stretching the graph vertically by a factor of {{{40}}}" means we go from {{{f(x)}}} to {{{40*f(x)}}}

"then shifting the graph of {{{f(x)}}} down {{{6}}} units" has us tacking on a "{{{-6}}}" like this: {{{40*f(x)-6}}}


"and finally shifting the graph right 5 units " tells us to replace '{{{x}}}' with '{{{x-5}}}' to get {{{40*f(x-5)-6}}}



Therefore, {{{g(x)=40*f(x-5)-6}}}

{{{f (x-5) = ((x-5)^2 -2(x-5) + 1)/20}}} 

{{{f (x-5) = (x^2-10x+25-2x+10 + 1)/20}}} 

{{{f (x-5) = (x^2-12x+36)/20}}} 

 {{{g(x)=40*(x^2-12x+36)/(20) -6}}}

{{{g(x)=cross(40)2*(x^2-12x+36)/cross(20) -6}}}

{{{g(x)=2(x^2-12x+36) -6}}}

{{{g(x)=2x^2-24x+72 -6}}}

{{{g(x)=2x^2-24x+66}}}


{{{drawing( 600, 600, -100, 100, -10, 100,grid(1), graph( 600, 600, -100, 100, -10, 100, 2x^2-24x+66,(x^2-2x + 1)/20)) }}}