Question

Compare Properties of Functions


The quadratic function f(x) has a vertex at (5, 4) and opens upward.

If g(x) = 3(x - 4)^2 + 5, which statement is true?

The maximum value of g(x) is greater than the maximum value of f(x).

The minimum value of g(x) is greater than the minimum value of f(x).

The minimum value of f(x) is greater than the minimum value of g(x).

The maximum value of f(x) is greater than the maximum value of g(x).

Answer 1

Okay, let me post a little chart real quick.

\(\large\color{ royalblue }{\large {\bbox[5pt, lightcyan ,border:2px solid white ]{ \large\text{ }\\
\begin{array}{|c|c|c|c|}
\hline \texttt{Shifts} ~~~\tt from~~~ {f(x)~~~\tt to~~~g(x)}&~\tt{c~~~units~~~~} \\
\hline
\\f(x)= x^2 ~~~~~\rm{\Rightarrow}~~~~ g(x)= (x \normalsize\color{red}{ -~\rm{c} })^2 &~\rm{to~~the~~right~} \\
\text{ } \\
f(x)= x^2 ~~~~~\rm{\Rightarrow}~~~~ g(x)= (x \normalsize\color{red}{ +~\rm{c} })^2&~\rm{to~~the~~left ~} \\
\text{ } \\
f(x)= x^2 ~~~~~\rm{\Rightarrow}~~~~ g(x)= x^2 \normalsize\color{red}{ +~\rm{c} } &~\rm{up~} \\
\text{ } \\
f(x)= x^2 ~~~~~\rm{\Rightarrow}~~~~ g(x)= x^2 \normalsize\color{red}{ -~\rm{c} } &~\rm{down~} \\ \\
\hline
\end{array} }}}\)

Answer 2

and same thing would apply with any coefficient m

\(\large\color{ teal }{\large {\bbox[5pt, lightcyan ,border:2px solid white ]{ \large\text{ }\\
\begin{array}{|c|c|c|c|}
\hline \texttt{Shifts} ~~~\tt from~~~ {f(x)~~~\tt to~~~g(x)}&~\tt{c~~~units~~~~} \\
\hline
\\f(x)= m{\tiny~}x^2 ~~~~~\rm{\Rightarrow}~~~~ g(x)= m{\tiny~}(x \normalsize\color{red}{ -~\rm{c} })^2 &~\rm{to~~the~~right~} \\
\text{ } \\
f(x)= m{\tiny~}x^2 ~~~~~\rm{\Rightarrow}~~~~ g(x)= m{\tiny~}(x \normalsize\color{red}{ +~\rm{c} })^2&~\rm{to~~the~~left ~} \\
\text{ } \\
f(x)= m{\tiny~}x^2 ~~~~~\rm{\Rightarrow}~~~~ g(x)= m{\tiny~}x^2 \normalsize\color{red}{ +~\rm{c} } &~\rm{up~} \\
\text{ } \\
f(x)= m{\tiny~}x^2 ~~~~~\rm{\Rightarrow}~~~~ g(x)= m{\tiny~}x^2 \normalsize\color{red}{ -~\rm{c} } &~\rm{down~} \\ \\
\hline
\end{array} }}}\)

Answer 3

getting free medals jk it's just a chart inside the box.

Answer 4

at the top the 3rd which it should be up

Answer 5

you are saying 3rd option or third row? excuse me, I am not sure what you mean...

Answer 6

3rd row

Answer 7

And just letting you know, that:

\(\normalsize\color{royalblue}{ \rm Opening~up~parabola }\) has \(\normalsize\color{red }{ \rm NO }\) absolute \(\normalsize\color{red }{ \rm ~maximum }\).
\(\normalsize\color{royalblue}{ \rm Opening~down~parabola }\) has has \(\normalsize\color{red }{ \rm NO }\) absolute \(\normalsize\color{red }{ \rm ~minimum }\).

Answer 8

(can be any even degree function that is opening down or up, doesn't have to be a parabola)

Answer 9

you need to find f(x)

Answer 10

`The quadratic function f(x) has a vertex at (5, 4) and opens upward.`

\(\normalsize\color{royalblue}{ \rm f(x)=a(x-h)^2+k }\)
where the vertex is: \(\normalsize\color{royalblue}{ \rm (h,k)}\)

so what is the vertex of f(x) and the f(x)?

Answer 11

i will go withC givin with the data above

Answer 12

keep disconnecting...

Answer 13

C is right