Answer:
(3, 0)
Explanation:
It might be first helpful to think about the function
, we will call this
. So,
.
The modulus (absolute value) function reflects any points on a graph that go below the x-axis up into the positive x region.
We know that the graph of
, will cross the x-axis at (3,0). We can work this out by setting y to 0 and rearranging for x. At the x-axis, y = 0.
Therefore, when the modulus comes in, a vertex will be created at (3,0).
But that is the vertex of
.
Using basic algebra we can derive from previous working that
.
Graphically, the multiplier of 2 on the outside of
stretches the graph in y-axis, and does so by the scale factor of 2.
With our vertex (3,0), the y value is 0. And if you multiply 0 and 2 together, 0 is produced. The x value will remain unchanged as a result of this transformation.
Therefore, the vertex of
is (3,0).