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.