Question

which equation is represented by the graph below?
answer
\\( y = 2|x + 3| - 6 \\) \\( y = 2|x + 3| + 6 \\)
\\( y = 2|x - 3| - 6 \\) \\( y = 2|x - 3| + 6 \\)

Explanation:

Step1: Identify vertex of V-shaped graph

The vertex is at (3, -6).

Step2: Recall vertex form of absolute value equation

Vertex form: $y = a|x - h| + k$, where (h,k) is vertex.

Step3: Substitute vertex into form

$y = a|x - 3| - 6$.

Step4: Find slope a using another point

Take point (6, 0): $0 = a|6 - 3| - 6 → 0 = 3a - 6 → a = 2$.

Step5: Write final equation

$y = 2|x - 3| - 6$.

Answer:

y = 2|x - 3| - 6