Question

the graph of f(x)=|x-h|+k contains the points (-6,-2) and (0,-2). the graph has a vertex at (h,-5). descrie how to find the value of h. then, explain how this value translates the graph of the parent function

Answer 1

h = -3

Translates the parent function 3 units to the left.

Explanation:

An absolute value function, f(x) = |x - h| + k, is a mathematical function that returns the non-negative magnitude (absolute value) of a real number x. Graphically, it is a V-shape with its vertex at (h, k), and is symmetric about the x-value of its vertex, x = h.

As the graph of the given function passes through two points (-6, -2) and (-0, -2) that have the same y-value of y = -2, and the function is symmetric about the x-value of its vertex, the value of h is the midpoint of the x-values of the two points:

`h=(-6-0)/(2)=(-6)/(2)=-3`

We are told that the graph has a vertex at (h, -5), so k = -5.

Substituting the values of h and k into the given function gives:

`f(x)=|x-(-3)|-5`

`f(x)=|x+3|-5`

This is a V-shaped graph, with a vertex at (-3, -5), symmetric about x = -3, and that passes through the points (-6, -2) and (0, -2).

The absolute value parent function is f(x) = |x|.

Adding "a" to the x value of the function translates the graph a units to the left. Therefore, as substituting h = -3 into the formula results in the addition of 3 to the x-value, the graph of the parent function has been translated 3 units to the left.

Subtracting k from the function translates the graph k units down. Therefore, as k = -5, this value translates the graph of the parent function 5 units down.