# What is the vertex form of  y= (2x-3)(7x-12)+17x^2-13x?

Jan 9, 2017

Vertex form of equation is $y = 31 {\left(x - \frac{29}{31}\right)}^{2} + \frac{275}{31}$

#### Explanation:

Vertex form of equation is $y = a {\left(x - h\right)}^{2} + k$

As we have $y = \left(2 x - 3\right) \left(7 x - 12\right) + 17 {x}^{2} - 13 x$

$= 2 x \times 7 x - 2 x \times 12 - 3 \times 7 x - 3 \times \left(- 12\right) + 17 {x}^{2} - 13 x$

$= 14 {x}^{2} - 24 x - 21 x + 36 + 17 {x}^{2} - 13 x$

$= 14 {x}^{2} - 24 x - 21 x + 36 + 17 {x}^{2} - 13 x$

$= 31 {x}^{2} - 58 x + 36$

$= 31 \left({x}^{2} - \frac{58}{31} x\right) + 36$

$= 31 \left({x}^{2} - 2 \times \frac{29}{31} x + {\left(\frac{29}{31}\right)}^{2}\right) + 36 - 31 \times {\left(\frac{29}{31}\right)}^{2}$

$= 31 {\left(x - \frac{29}{31}\right)}^{2} + 36 - \frac{841}{31}$

$= 31 {\left(x - \frac{29}{31}\right)}^{2} + \frac{275}{31}$
graph{(2x-3)(7x-12)+17x^2-13x [-5, 5, -2.88, 37.12]}