Question

value: 1

find the vertex of the function \\(y = |x + 3|\\).

a. \\((3, 0)\\)
b. \\((-3, 0)\\)
c. \\((0, 3)\\)
d. \\((0, -3)\\)

Explanation:

Identify the parent function and its vertex

$$ y = |x| \implies \text{Vertex} = (0, 0) $$

Apply horizontal translation

$$ y = |x + 3| \implies h = -3 $$

Determine the new vertex coordinates

$$ (x - h, y + k) \implies (0 - 3, 0 + 0) = (-3, 0) $$

Answer:

• a. (3, 0)
• b. (-3, 0) (Correct answer)
• c. (0, 3)
• d. (0, -3)