Question

What are the coordinates of the vertex of the graph of:

f(x) = 2 lx - 3l

Enter your answer in the boxes.

( ), ( )

Answer 1

(3, 0)

Explanation:

It might be first helpful to think about the function
`|x-3|`, we will call this
`g(x)`. So,
`g(x)=|x-3|`.

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
`y=x-3`, 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
`g(x)`.

Using basic algebra we can derive from previous working that
`f(x)=2g(x)`.

Graphically, the multiplier of 2 on the outside of
`g(x)` 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
`f(x)` is (3,0).