let the graph of g be a horizontal shrink by a factor of 2/3, followed by a transiation 5 units left and 2 units down of the graph of f(x)=x^2, write a rule for g

Question

let the graph of g be a horizontal shrink by a factor of 2/3, followed by a transiation 5 units left and 2 units down of the graph of f(x)=x^2, write a rule for g

Answer 1

g(x)= a(x-h)^2 +k where (h,k)= vertex

= minimum point of the parabola

original vertex is (0,0) for f(x)=x^2

new vertex is (-2,-2)

g(x)=(3/2)f(x--2)-2

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

add 2 to x for shift 2 left

subtract 2 for shift 2 down

increase coefficient of f(x) by factor of 3/2

for horizontal shrinkage of 2/3= vertical stretch of 3/2