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

Mar 5, 2016

Axis of symmetry is parallel to y-axis, x = $\frac{3}{2}$.
Minimum y = $- \frac{13}{4}$.
y increases from $- \frac{13}{4}$ without limit.

#### Explanation:

${\left(x - \frac{5}{2}\right)}^{2} = y - \frac{13}{4}$.
This represents the parabola with vertex at $\left(\frac{5}{2} , - \frac{13}{4}\right)$, with axis of symmetry parallel to y-axis x = 3/2.
$\frac{\mathrm{dy}}{\mathrm{dx}} = 2 x - 5 = 0 \to x = \frac{5}{2}$.
$\frac{{d}^{2} y}{{\mathrm{dx}}^{2}} = 2 > 0 \to$ y is min, when x=5/2.
There is no maximum.