Question

1. $y = -2|x + 2|$

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 $y = -2|x + 2|$, this is $y = -2|x - (-2)| + 0$, so vertex is $(-2, 0)$.

Step2: Find x-intercept (set y=0)

Set $0 = -2|x + 2|$
Divide both sides by $-2$: $0 = |x + 2|$
Solve for $x$: $x + 2 = 0 \implies x = -2$
So x-intercept is $(-2, 0)$ (same as vertex).

Step3: Find y-intercept (set x=0)

Substitute $x=0$: $y = -2|0 + 2| = -2|2| = -2 \times 2 = -4$
So y-intercept is $(0, -4)$.

Step4: Find additional point (x=-4)

Substitute $x=-4$: $y = -2|-4 + 2| = -2|-2| = -2 \times 2 = -4$
So point is $(-4, -4)$.

Step5: Plot points and draw graph

Plot $(-2,0)$, $(0,-4)$, $(-4,-4)$, then draw a V-shaped graph opening downward (since $a=-2 < 0$) passing through these points.

Answer:

The graph is a downward-opening V with vertex at $(-2, 0)$, passing through $(0, -4)$ and $(-4, -4)$. When plotted on the grid, these points connect to form the absolute value function $y = -2|x + 2|$.