# What is the vertex form of y=17x^2+88x+1?

Jul 30, 2017

$y = 17 \left(x + \frac{44}{17}\right) - \frac{1919}{17}$

#### Explanation:

Given -

$y = 17 {x}^{2} + 88 x + 1$

Vertex
x-coordinate of the vertex

$x = \frac{- b}{2 a} = \frac{- 88}{2 \times 17} = \frac{- 88}{34} = \frac{- 44}{17}$

y-coordinate of the vertex

$y = 17 {\left(\frac{- 44}{17}\right)}^{2} + 88 \left(\frac{- 44}{17}\right) + 1$
$y = 17 \left(\frac{1936}{289}\right) - \frac{3872}{17} + 1$
$y = \frac{32912}{289} - \frac{3872}{17} + 1$
$y = \frac{32912 - 65824 + 289}{289} = \frac{- 32623}{289} = \frac{- 1919}{17}$

The vertex form of the equation is

$y = a {\left(x - h\right)}^{2} + k$

$a = 17$ coefficient of ${x}^{2}$
$h = \frac{- 44}{17}$ x coordinate of the vertex
$k = \frac{- 1919}{17}$ y-coordinate of the vertex

$y = 17 \left(x + \frac{44}{17}\right) - \frac{1919}{17}$