# How do you write the quadratic in vertex form given x^2-7x + 9?

$\left(- \frac{b}{2 a}\right) = \frac{7}{2}$
$f \left(- \frac{b}{2 a}\right) = \frac{49}{4} - \frac{49}{2} + 9 = - \frac{49}{4} + 9 = - \frac{13}{4}$
Factored form: $f \left(x\right) = {\left(x - \frac{7}{2}\right)}^{2} - \frac{13}{4}$
Check. Develop $f \left(x\right) = {x}^{2} - 7 x + \frac{49}{4} - \frac{13}{4} = {x}^{2} - 7 x + 9$. Correct