Question

Hello, I you could please help with number 17? Im not sure on how to do theseThanks

Answer 1

17. we are given the equation

`f(x)=(x-4)^2-1`

Vertex = (4, -1)

To get the x-intercept

`\begin{gathered} Put\text{ f\lparen x\rparen = 0} \\ f(x)=(x-4)^2-1 \\ 0=(x-4)^2-1 \\ (x-4)^2=1 \\ Taking\text{ the square root of both sides} \\ (x-4)^=\pm1 \\ x=4\pm1 \\ \\ x=5,3 \\ so\text{ we have} \\ (5,0),(3,0) \end{gathered}`

The graph is

Domain = the set of real number

`\begin{gathered} Domain=(-\infty,\infty) \\ Range=[-1,\infty) \end{gathered}`