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

Mar 22, 2016

The axis of symmetry is at $x = \frac{5}{2}$ and the minimum value is $y = - \frac{13}{4}$.

#### Explanation:

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

$y = {x}^{2} - 5 x + 3$
$y = {\left(x - \frac{5}{2}\right)}^{2} - \frac{25}{4} + 3$
$y = {\left(x - \frac{5}{2}\right)}^{2} - \frac{13}{4}$

The axis of symmetry is therefore at $x = \frac{5}{2}$ and the minimum value is $y = - \frac{13}{4}$. This is a minimum because the squared term is positive.