Question

the standard form of an absolute value function is $f(x)=a|x - h|+k$. which of the following represents the vertex?
$(-k, h)$
$(-h, k)$
$(k, h)$
$(h, k)$

Explanation:

Step1: Recall Vertex Form Rule

For absolute value function \( f(x) = a|x - h| + k \), the vertex is at \( (h, k) \) by definition of the standard form.

Step2: Match with Options

Check each option:

• \((-k, h)\): Incorrect.
• \((-h, k)\): Incorrect.
• \((k, h)\): Incorrect.
• \((h, k)\): Matches the rule.

Answer:

D. (h, k)