What is the the vertex of #y =-4x^2+2x+1 #?

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Answer 1 · 2016-01-04T03:28:05

#(1/4, 5/4)#

where #(h, k)# is the vertex of the quadratic.

To put the equation into vertex form, we can use a process called completing the square.

#y = -4x^2 + 2x + 1#

#= -4(x^2 - 1/2x) + 1#

#= -4(x^2 -1/2x +1/16 - 1/16) +1#

#=-4(x^2 - 1/2x +1/16) + 1/4 + 1#

#=4(x-1/4)^2 + 5/4#

Thus the vertex is #(1/4, 5/4)#