# What is the vertex form of y= (x + 1)(x + 10) ?

Feb 21, 2016

$y = {\left(x + \frac{11}{2}\right)}^{2} - \frac{81}{4}$

#### Explanation:

The standard form of a quadratic function is $y = a {x}^{2} + b x + c$

Before we get to vertex form , require to distribute the brackets.

hence (x + 1 )(x + 10 ) $= {x}^{2} + 11 x + 10$

This is now in standard form and by comparison with $a {x}^{2} + b x + c$

we obtain: a = 1 , b = 11 and c = 10

The vertex form of the equation is $y = a {\left(x - h\right)}^{2} + k$
where (h , k ) are the coords of vertex.

x-coord of vertex (h)$= \frac{- b}{2 a} = - \frac{11}{2}$

and y-coord (k) = ${\left(- \frac{11}{2}\right)}^{2} + 11 \left(- \frac{11}{2}\right) + 10 = \frac{121}{4} - \frac{121}{2} + 10 = - \frac{81}{4}$
hence a = 1 and (h , k ) $= \left(- \frac{11}{2} , - \frac{81}{4}\right)$

$\Rightarrow y = {\left(x + \frac{11}{2}\right)}^{2} - \frac{81}{4}$