# How do you write f(x) = x^2 - 3x + 1  in vertex form and identify the vertex?

x o vertex: $x = \left(- \frac{b}{2} a\right) = \frac{3}{2}$
y of vertex:$f \left(\frac{3}{2}\right) = \frac{9}{4} - \frac{9}{2} + 1 = - \frac{5}{4}$
Vertex form:$f \left(x\right) = {\left(x - \frac{3}{2}\right)}^{2} - \frac{5}{4}$
Check by developing:$f \left(x\right) = {x}^{2} - 3 x + \frac{9}{4} - \frac{5}{4} = {x}^{2} - 3 x + 1$ .OK