18. $f(x)=2(x-1)^{2}+4$ and $g(x)=2(x+3)^{2}+1$. Describe the transformation of $f(x)$ to $g(x)$ ?
Answer
\(\boxed{\text{The transformation from } f(x) \text{ to } g(x) \text{ is a shift of 4 units to the left and 3 units down.}}\)
Step 1 ：The function \(f(x)\) is a parabola with vertex at \((1,4)\) and the function \(g(x)\) is a parabola with vertex at \((-3,1)\).
Step 2 ：Comparing the two functions, we can see that the vertex of the parabola has moved from \((1,4)\) to \((-3,1)\). This indicates a shift of 4 units to the left and 3 units down.
Step 3 ：The coefficient of the squared term in both functions is 2, which means there is no vertical stretch or compression.
Step 4 ：\(\boxed{\text{The transformation from } f(x) \text{ to } g(x) \text{ is a shift of 4 units to the left and 3 units down.}}\)
