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

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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.