What is the vertex form of y= (x+6)(x-23)?

Jul 24, 2017

${\left(x - \frac{17}{2}\right)}^{2} - \frac{825}{4}$

And the vertex is the point $A \left(\frac{17}{2} , \frac{825}{4}\right)$

Explanation:

$y = \left(x + 6\right) \left(x - 23\right) = {x}^{2} - 17 x - 138 =$

${x}^{2} - 2 \cdot \frac{17}{2} x - 138 = {x}^{2} - 2 \cdot \frac{17}{2} x + {\left(\frac{17}{2}\right)}^{2} - {\left(\frac{17}{2}\right)}^{2} - 138 =$

${\left(x - \frac{17}{2}\right)}^{2} - \frac{825}{4}$

And the vertex is the point $A \left(\frac{17}{2} , \frac{825}{4}\right)$