the graph of f(x) = |x - h| + k contains the points (-6, -2) and (0, -2). the graph has a vertex at (h, -5)…

Explanation:

Step1: Note the symmetry of absolute - value function

The graph of (y = |x - h|+k) is symmetric about the vertical line (x = h). Since the points ((-6,-2)) and ((0,-2)) have the same (y) - value, the axis of symmetry (x = h) is the mid - point of the (x) - coordinates of these two points.

Step2: Calculate the value of (h)

The formula for the mid - point of two numbers (x_1) and (x_2) is (h=\frac{x_1 + x_2}{2}). Here, (x_1=-6) and (x_2 = 0), so (h=\frac{-6 + 0}{2}=-3).

Step3: Explain the translation

The parent function of (y=|x - h|+k) is (y = |x|). The value of (h=-3) means the graph of the parent function (y = |x|) is translated 3 units to the left.

Answer:

To find (h), use the fact that the axis of symmetry of the absolute - value function (y = |x - h|+k) is the mid - point of the (x) - coordinates of two points with the same (y) - value. For the points ((-6,-2)) and ((0,-2)), (h=\frac{-6 + 0}{2}=-3). The graph of the parent function (y = |x|) is translated 3 units to the left.