Question

The graph of an absolute value function p(x)
has the following key features:

p(x)
is increasing for x≥−4
p(x)
is decreasing for x≤−4
The domain for p(x)
is all real numbers
The range for p(x)
is x≥2
(1 point)
Write the equation for the absolute value function in vertex form.

Answer 1

Vertex is at (-4, 2) (decreasing left of -4, increasing right, minimum 2). In vertex form:
p(x) = a|x + 4| + 2.
With the standard slope a = 1, p(x) = |x + 4| + 2.