Question

sketch a graph of: $f(x) = -2|x + 4| + 1$
before sketching the graph, determine where the function has its minimum or
place your first point there. think in terms of transformations of the parent fun
graph.
question help: video 1 video 2

Explanation:

Step1: Find vertex (max point)

The vertex of $f(x)=a|x-h|+k$ is $(h,k)$. For $f(x)=-2|x+4|+1$, rewrite as $f(x)=-2|x-(-4)|+1$, so vertex is $(-4,1)$. This is the maximum since $a=-2<0$.

Step2: Find left side point

Choose $x=-5$, substitute into $f(x)$:
$f(-5)=-2|-5+4|+1=-2|{-1}|+1=-2(1)+1=-1$
Point: $(-5,-1)$

Step3: Find right side point

Choose $x=-3$, substitute into $f(x)$:
$f(-3)=-2|-3+4|+1=-2|1|+1=-2(1)+1=-1$
Point: $(-3,-1)$

Step4: Plot and connect points

Plot $(-4,1)$, $(-5,-1)$, $(-3,-1)$, then draw two lines from the vertex through each outer point, forming an downward-opening V-shape.

Answer:

The graph is a downward-opening V with vertex (maximum point) at $(-4, 1)$, passing through $(-5, -1)$ and $(-3, -1)$.