Answer: (0.2, - 7)
Procedure:
1) The parent function is f(x) = |x| whose vertex is (0,0)
2) The vertex of a g(x) function g(x) = |10x - 2| will be where |10x - 2| = 0
From which, you can solve for x: |10x - 2| = 0 => 10x - 2 = 0 => 10x = 2 => x = 2/10 = 0.2.
Meaning that the vertex of g(x) is (0.2, 0)
3) The vertex of function h(x) = |10x - 2| - 7 will be the vertex of the function g(x) = |10x - 2| translated 7 units downward.
So the x-coordinate of this vertex will be the same of that fro g(x), i.e. 0.2, and the y-coordinate will be 0 - 7 = - 7.
So, the new vertex, without having looking the graph, is (0.2, - 7).
You may now graph the function and verify this answer.
