Question

What is the vertex of the function h(x) = |x + 6| - 3?

a) (-6, -3)
b) (-6, 3)
c) (6, 3)
d) (6, -3)

Answer 1

The vertex of the function h(x) = |x + 6| - 3 is at the point (-6, -3), option a.

Step-by-step explanation:

The vertex of the function h(x) = |x + 6| - 3 is the point where the expression inside the absolute value reaches zero since this is where the graph changes direction. In this case, the expression inside the absolute value, x + 6, is zero when x = -6. Substituting x = -6 into the function gives us h(-6) = |-6 + 6| - 3 = |0| - 3 = 0 - 3 = -3. Therefore, the vertex of the function is at the point (-6, -3).