Question

graph the following absolute value expression:
$y = 3|-x|$
show your work here

Explanation:

Step1: Simplify the absolute value

Recall that $|-x| = |x|$, so the equation simplifies to:
$y = 3|x|$

Step2: Identify the vertex

The vertex of $y=a|x-h|+k$ is $(h,k)$. For $y=3|x|$, $h=0, k=0$, so vertex is:
$(0, 0)$

Step3: Find points for $x>0$

For $x>0$, $|x|=x$, so $y=3x$.

• When $x=2$, $y=3(2)=6$, point: $(2, 6)$
• When $x=4$, $y=3(4)=12$, point: $(4, 12)$

Step4: Find points for $x<0$

For $x<0$, $|x|=-x$, so $y=3(-x)=-3x$.

• When $x=-2$, $y=-3(-2)=6$, point: $(-2, 6)$
• When $x=-4$, $y=-3(-4)=12$, point: $(-4, 12)$

Step5: Plot and connect points

Plot the vertex $(0,0)$, $(2,6)$, $(4,12)$, $(-2,6)$, $(-4,12)$, then draw two straight lines from the vertex through these points, forming a V-shape opening upward.

Answer:

The graph is a V-shaped absolute value curve with vertex at $(0,0)$, passing through points $(-4,12)$, $(-2,6)$, $(2,6)$, $(4,12)$, opening upward.