Question

How do you find the axis of symmetry, and the maximum or minimum value of the function `y=x^2-5x+3`?

Answer 1

The axis of symmetry is at `x=5/2` and the minimum value is `y=-13/4`.

Explanation:

Reformat the expression by completing the square. This will identify the vertex and hence the axis of symmetry and the maximum/minimum value.

`y = x^2 -5x+3`
`y=(x-5/2)^2 - 25/4 +3`
`y=(x-5/2)^2 -13/4`

The axis of symmetry is therefore at `x=5/2` and the minimum value is `y=-13/4`. This is a minimum because the squared term is positive.