How do you find the coordinates of the vertex #y= 2x^2 + 7x - 21 #?

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Answer 1 · 2017-04-04T04:42:46

Vertex is #(-7/4,-217/8)# or #(-1 3/4,-27 1/8)#

To find the coordinates of vertex of #y=2x^2+7x-21#, one should convert this equation into vertex form i.e.

#(y-k)=a(x-h)^2#, where vertex is #(h,k)#

Now #y=2x^2+7x-21#

#hArry=2(x^2+7/2x)-21#

#=2(x^2+2xx7/4xx x+(7/4)^2-(7/4)^2)-21#

#=2((x+7/4)^2-(7/4)^2)-21#

#=2(x+7/4)^2-2xx49/16-21#

#=2(x+7/4)^2-49/8-21#

#=2(x+7/4)^2-217/8#

or #(y+217/8)=2(x+7/4)^2#

Hence, vertex is #(-7/4,-217/8)# or #(-1 3/4,-27 1/8)#

graph{2x^2+7x-21 [-6, 4, -28.56, -8.56]}