Question

graph the equation.
$y = 5|x + 6|$

Explanation:

Step1: Find the vertex of the absolute value function

The vertex form of an absolute value function is $y=a|x-h|+k$, where $(h,k)$ is the vertex. For $y=5|x+6|$, rewrite it as $y=5|x-(-6)|+0$. So the vertex is $(-6, 0)$.

Step2: Find a point for $x > -6$

Choose $x=-4$. Substitute into the equation:
$y=5|-4+6|=5|2|=5\times2=10$
This gives the point $(-4, 10)$.

Step3: Find a point for $x < -6$

Choose $x=-8$. Substitute into the equation:
$y=5|-8+6|=5|-2|=5\times2=10$
This gives the point $(-8, 10)$.

Step4: Plot and draw the graph

Plot the vertex $(-6,0)$, along with $(-4,10)$ and $(-8,10)$. Draw two straight lines: one connecting $(-6,0)$ to $(-4,10)$ (extending right), and another connecting $(-6,0)$ to $(-8,10)$ (extending left).

Answer:

The graph is a V-shaped absolute value curve with vertex at $(-6, 0)$, passing through $(-4, 10)$ and $(-8, 10)$, opening upwards with a slope of $5$ for $x > -6$ and $-5$ for $x < -6$.