What is the vertex of #y= −4x^2 -7x + 1 #?

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Answer 1 · 2017-05-23T04:08:18

From vertex form, the vertex is at #(-7/8 , 65/16)#, which can be written as #(-.875, 4.0625)#

#y = -4x^2-7x+1#

Factor out the #-4#
#y= -4 [x^2 + 7/4x -1/4]#

#y = -4 [(x+7/8x)^2-49/64 - 1/4]#

#y = -4 [(x+7/8x)^2-(49 + 16)/64]#

#y = -4 [(x+7/8)^2 - 65/64]#

#y = -4(x+ 7/8)^2 + 65/16#

From vertex form, the vertex is at #(-7/8 , 65/16)#, which can be written as #(-.875, 4.0625)#