Question

Given that h(x)=(x-4)^2+2,write an equation for g(x) in terms of x.

Answer 1

Step-by-step explanation

We can use the following rules of transformation of functions:

• f(x - h) moves the function h units right.

• f(x + h) moves the function h units left.

• f(x) + k moves the function k units up.

• f(x) - k moves the function k units down.

From the graph of h(x), we can determine the parent function and then transform it to obtain the graph of g(x).

Analyzing the graph of h(x), we have:

`\begin{gathered} h(x)=(x-4)^2+2 \\ h=4\Rightarrow\text{ The graph of f\lparen x\rparen has moved 4 units to the right.} \\ k=2\Rightarrow\text{ The graph of f\lparen x\rparen has moved 2 units up.} \\ \text{ Then} \\ f(x)=x^2\Rightarrow\text{ Parent function} \end{gathered}`

Now, we can obtain the graph of g(x):

Answer
`g(x)=(x+6)^(2)-6`