Question

the graph of g(x) = |x - h| + k is shown in the coordinate grid. what must be true about the signs of h and k? both h and k must be positive. both h and k must be negative. h must be positive and k must be negative. h must be negative and k must be positive.

Explanation:

Step1: Recall vertex form of absolute value

The function \( g(x) = |x - h| + k \) has its vertex at \( (h, k) \).

Step2: Analyze the graph's vertex position

From the graph, the vertex is in the second quadrant (left of y - axis, above x - axis). In the second quadrant, the x - coordinate (h) is negative (since it's left of y - axis, \( x<0 \)) and the y - coordinate (k) is positive (since it's above x - axis, \( y > 0 \)). So h must be negative and k must be positive.

Answer:

D. \( h \) must be negative and \( k \) must be positive.