We start with the basic 

f(x) = x², which has this red graph:



Then we move the red graph of f(x) 3 units left, 
by replacing x by (x+3) and getting

g(x) = (x+3)², which has this green graph:



 
Then we move the green graph of g(x) 8 units down, 
by subtracting 8 from the right side of g(x), getting

h(x) = (x+3)²-9, which has this blue graph:



Then we flip the blue graph of h(x) over the x-axis, 
by multiplying the right side of h(x) by -1, getting

i(x) = -(x+3)²+9, which has this purplish lavender graph:



Finally we stretch the purplish lavender graph of i(x) vertically by a 
factor of 5, by multiplying the right side of i(x) by 5, 
getting

j(x) = -5(x+3)²+45, which has this long light yellow-green-grayish graph:




Edwin