Question

Use the function to answer the question.

f(x) = 4|x + 1| – 6

What is the vertex of the graph of f(x)?

(–1, –6)
(–1, 6)
(1, –6) <--what i picked
(4, –6)

Answer 1

So for parent function, \(\large\color{black}{ \rm y=4\left| x \right| }\) the vertex is (0,0). Your function though is shifted.
Find out the shift based on the rules bloew, for me please.

Rules of \(\large\color{black}{ \rm shifts }\) from \(\large\color{black}{ \rm f(x) }\) to \(\large\color{black}{ \rm g(x) }\).


\(\large\color{black}{ \rm f(x)=4\left| x \right| ~~~~~~~~~\rm{\Longrightarrow}~~~~~~~~\rm g(x)=4\left| x \color{blue}{ -~\rm{c} }\right| }\)
\(\large\color{blue}{ ~\rm {c} }\) units to the \(\normalsize\color{blue}{ \rm right }\).


\(\large\color{black}{ \rm f(x)=4\left| x \right| ~~~~~~~~~\rm{\Longrightarrow}~~~~~~~~\rm g(x)=4\left| x \color{blue}{ +~\rm{c} }\right| }\)
\(\large\color{blue}{ ~\rm {c} }\) units to the \(\normalsize\color{blue}{ \rm left }\).


\(\large\color{black}{ \rm f(x)=4\left| x \right| ~~~~~~~~~\rm{\Longrightarrow}~~~~~~~~\rm g(x)=4\left| x \right| \color{blue}{ +~\rm{c} }}\)
\(\large\color{blue}{ ~\rm {c} }\) units \(\normalsize\color{blue}{ \rm up }\).


\(\large\color{black}{ \rm f(x)=4\left| x \right| ~~~~~~~~~\rm{\Longrightarrow}~~~~~~~~\rm g(x)=4\left| x \right| \color{blue}{ -~\rm{c} }}\)
\(\large\color{blue}{ ~\rm{c} }\) units \(\normalsize\color{blue}{ \rm down }\).

if you have questions please ask.