Question

graph the equation.
$y = -3|x| - 4$

Explanation:

Step1: Identify vertex of absolute value function

The vertex form of an absolute value function is $y=a|x-h|+k$, where $(h,k)$ is the vertex. For $y=-3|x|-4$, $h=0$, $k=-4$. So vertex is $(0, -4)$.

Step2: Find x=1, x=-1 points

For $x=1$: $y=-3|1|-4=-3-4=-7$, so point $(1, -7)$.
For $x=-1$: $y=-3|-1|-4=-3-4=-7$, so point $(-1, -7)$.

Step3: Find x=2, x=-2 points

For $x=2$: $y=-3|2|-4=-6-4=-10$, so point $(2, -10)$.
For $x=-2$: $y=-3|-2|-4=-6-4=-10$, so point $(-2, -10)$.

Step4: Plot points and draw graph

Plot the vertex $(0,-4)$, $(1,-7)$, $(-1,-7)$, $(2,-10)$, $(-2,-10)$, then draw two straight lines from the vertex through these points, forming a downward-opening V-shape.

Answer:

The graph is a downward-opening V with vertex at $(0, -4)$, passing through points $(\pm1, -7)$ and $(\pm2, -10)$, extending infinitely along the lines $y=-3x-4$ (for $x\geq0$) and $y=3x-4$ (for $x<0$).