Answer
See the graph
Work Step by Step
Given: $y=3(x+4)^2+7$
The function is in vertex form $y=x(x-h)^2+k$
with $a=3, h=-4,k=7$
Hence, the vertex is $(-4,7)$
The axis of symmetry is $x=-4$
Find some other points:
$x=-6 \rightarrow y=19$
$x=-5 \rightarrow y=10$
$x=-3 \rightarrow y=10$
$x=-2 \rightarrow y=19$