# What is the vertex form of y= (25x + 1)(x - 1) ?

May 8, 2017

$y = 25 {\left(x - \frac{12}{25}\right)}^{2} + \frac{169}{25} \leftarrow$ this is the vertex form.

#### Explanation:

Multiply the factors:

$y = 25 {x}^{2} - 24 x - 1$

Comparing the standard form, $y = a {x}^{2} + b x + c$, we observe that $a = 25 , b = - 24 \mathmr{and} c = - 1$

We know that equation for the coordinate of the vertex is:

$h = - \frac{b}{2 a}$

Substituting the values:

$h = - \frac{- 24}{2 \left(25\right)}$

$h = \frac{12}{25}$

We know that the y coordinate of vertex, k, is the function evaluated at $x = h$

$k = 25 {h}^{2} - 24 h - 1$

$k = 25 {\left(\frac{12}{25}\right)}^{2} - 24 \left(\frac{12}{25}\right) - 1$

$k = \frac{169}{25}$

The vertex form is:

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

Substitute in the known values:

$y = 25 {\left(x - \frac{12}{25}\right)}^{2} + \frac{169}{25} \leftarrow$ this is the vertex form.