What is the vertex form of y=7x^2-14x-6 ?

Jun 16, 2018

$y = 7 {\left(x - 2\right)}^{2} - 13$

Explanation:

$y = 7 {x}^{2} - 14 x - 6$

$y + 6 = 7 {x}^{2} - 14 x$

$y + 6 = 7 \left({x}^{2} - 2 x\right)$

$y + 6 + 7 c = 7 \left({x}^{2} - 2 x + c\right)$

$c = {\left(- \frac{2}{2}\right)}^{2} = 1$

$y + 6 + 7 \cdot 1 = 7 \left({x}^{2} - 2 x + 1\right)$

$y + 13 = 7 {\left(x - 2\right)}^{2}$

$y = 7 {\left(x - 2\right)}^{2} - 13$