Question

How do you find the vertex of `y = x^2 – 6x + 5`?

Answer 1

Complete the square

Explanation:

After completing the square,

`y = x^2 - 6x + 5`

`= (x - 3)^2 - 4`

Here is a graph of `y = x^2 - 6x + 5`.
graph{x^2 - 6x + 5 [-2, 8, -5, 5]}
We can see (either graphically or algebraically) that the lowest point, or minimum, occurs when `x = 3` and `y = -4`. That is the location of the vertex.

The coordinate of the vertex is `(3,-4)`.