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

Question

1572 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-08T21:49:16

$y = 25(x-12/25)^2+169/25 larr$ this is the vertex form.

Multiply the factors:

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

Comparing the standard form, $y = ax^2+bx+c$ , we observe that $a = 25, b = -24 and c = -1$

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

$h = -b/(2a)$

Substituting the values:

$h = -(-24)/(2(25))$

$h = 12/25$

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

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

$k = 25(12/25)^2-24(12/25)-1$

$k = 169/25$

The vertex form is:

$y = a(x-h)^2+k$

Substitute in the known values:

$y = 25(x-12/25)^2+169/25 larr$ this is the vertex form.

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