Question 1118148
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The original function is {{{y = x^2}}}.<br>
(1) dilated in the x direction by a factor of 5: replace x with x/5:  {{{y = (x/5)^2}}}<br>
(2) dilated in the y direction by a factor of 2: replace y with y/2:  {{{y/2 = (x/5)^2}}}, or {{{y = 2(x/5)^2}}}<br>
(3) translated 3 to the right: replace x with x-3:  {{{y = 2((x-3)/5)^2}}}<br>
(4) translated 4 up: add 4 to y: {{{y = 2((x-3)/5)^2+4}}}<br>
A graph:<br>
red: basic function
green: dilated by a factor of 5 in the x direction (red, 1/5 as steep)
blue: dilated by a factor of 2 in the y direction (green, 2 times as steep)
purple: translated 3 to the right (blue, moved right 3)
yellow: translated 4 up (purple, moved up 4)<br>
{{{graph(400,400,-10,10,-4,10,x^2,(x/5)^2,2(x/5)^2,2((x-3)/5)^2,2((x-3)/5)^2+4)}}}