# How do you write the quadratic in vertex form given y=-2x^2+6x+1?

Standard form$f \left(x\right) = - 2 {x}^{2} + 6 x + 1$
Vertex form $f \left(x\right) = {\left(x - \frac{b}{2 a}\right)}^{2} + f \left(- \frac{b}{2 a}\right)$
$- \frac{b}{2} a = - \frac{6}{-} 4 = \frac{3}{2}$
$f \left(\frac{3}{2}\right) = - 2 \left(\frac{9}{4}\right) + 6 \left(\frac{3}{2}\right) + 1 = \frac{11}{2}$
Vertex form$f \left(x\right) = {\left(x - \frac{3}{2}\right)}^{2} + \frac{11}{2}$