What is the vertex form of y= (2x-3)(x+5)-12x?

Mar 21, 2017

Explained below

Explanation:

y=(2x-3)(x+5)

= $2 {x}^{2} + 7 x - 15 - 12 x$

=$2 {x}^{2} - 5 x - 15$

=$2 \left({x}^{2} - \frac{5}{2} x\right) - 15$

=$2 \left({x}^{2} - \frac{5}{2} x + \frac{25}{16} - \frac{25}{16}\right) - 15$

=$2 {\left(x - \frac{5}{4}\right)}^{2} - 15 - \frac{25}{8}$

=$2 {\left(x - \frac{5}{2}\right)}^{2} - \frac{145}{8}$

This the required vertex form . Vertex is$\left(\frac{5}{2} , - \frac{145}{8}\right)$