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

1 Answer
Mar 22, 2016

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.