Question

Given the function f(x) = 4(x + 1)2 − 3, indicate the shifts that will affect the location of the vertex, and explain what effect they will have. Use complete sentences.

f(x−2)
f(x) − 2
f(2x)
2•f(x)

Answer 1

hint:
we can rewrite yuour equation as follows:
\[\Large y + 3 = 4{\left( {x + 1} \right)^2}\]

Answer 2

where y=f(x)

Answer 3

now we perform this traslation:
\[\Large \left\{ \begin{gathered}
Y = y + 3 \hfill \\
X = x + 1 \hfill \\
\end{gathered} \right.\]
where X, ad Y are the new coordinates. after that traslation, we can rewrite your equation as follows:
\[\Large Y = 4{X^2}\]
Now do you know what is the graph of the function
Y= 4 X^2 ?