# What is the vertex form of y= 35x^2 - 22x + 3 ?

the vertex form
${\left(x - \frac{11}{35}\right)}^{2} = \frac{1}{35} \left(y - - \frac{16}{35}\right)$

#### Explanation:

From the given, perform completing the square
$y = 35 {x}^{2} - 22 x + 3$

$y = 35 \left({x}^{2} - \frac{22}{35} x\right) + 3$

Determine the constant to added and subtracted by using the numerical coefficient of x which 22/35. We divide 22/35 by 2 then square it$= {\left(\frac{22}{35} \div 2\right)}^{2} = \frac{121}{1225}$

$y = 35 \left({x}^{2} - \frac{22}{35} x + \frac{121}{1225} - \frac{121}{1225}\right) + 3$

$y = 35 \left({x}^{2} - \frac{22}{35} x + \frac{121}{1225}\right) - 35 \cdot \frac{121}{1225} + 3$

$y = 35 {\left(x - \frac{11}{35}\right)}^{2} - \frac{121}{35} + 3$

$y = 35 {\left(x - \frac{11}{35}\right)}^{2} + \frac{- 121 + 105}{35}$

$y = 35 {\left(x - \frac{11}{35}\right)}^{2} - \frac{16}{35}$

$y + \frac{16}{35} = 35 {\left(x - \frac{11}{35}\right)}^{2}$

${\left(x - \frac{11}{35}\right)}^{2} = \frac{1}{35} \left(y - - \frac{16}{35}\right)$

God bless....I hope the explanation is useful.