# How do you write the quadratic in vertex form given y=2x^2-10x+5?

Vertex form$f \left(x\right) = {\left(x - \frac{b}{2 a}\right)}^{2} + f \left(- \frac{b}{2 a}\right)$
$- \frac{b}{2} a = \frac{10}{4} = \frac{5}{2}$
$f \left(\frac{5}{4}\right) = 2 \left(\frac{25}{4}\right) - 10 \left(\frac{5}{2}\right) + 5 = - \frac{15}{2}$
Vertex form $f \left(x\right) = {\left(x - \frac{5}{2}\right)}^{2} - \frac{15}{2}$