Answer with explanation:
The given function is
f(x)=x²
y=x²
The vertex of the Original parabolic function is ,(0,0).
The graph of transformed function is:
[tex]g(x)=4 x^2 +24 x+30\\\\g(x)=4 \times (x^2+6 x+\frac{30}{4})\\\\y=4 \times [(x+3)^2-9+\frac{30}{4}]\\\\y=4 \times [(x+3)^2-\frac{6}{4}]\\\\y=4 \times (x+3)^2-6\\\\y+6=4 \times [(x+3)^2][/tex]
The Vertex of the transformed parabolic function is, (-3, -6).
So, the original function is transformed 3 units horizontally left, 6 units Vertically down and shrank vertically by a factor of 4.
