What is the vertex of # y= -x^2 +9x - 8#?

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Answer 1 · 2017-07-26T00:59:55

Vertex: #(9/2,49/4)#

Apply the vertex formula: #x=-b/(2a)#, where #a=-1# and #b=9#

Thus,

#x=-(9)/(2(-1))#

#x=9/2#

We must now find the #y#-value for the vertex which we can find by substituting #9/2# for #x# in the given equation #y=-x^2+9x-8#. So...

#-(9/2)^2+9(9/2)-8#

#y=-81/4+81/2-8#

Find the LCD of #4,2# and #1#; that is #4#

#y=-81/4+(81times2)/(2times2)-(8times4)/(1times4)#

#y=-81/4+162/4-32/4#

#y=(-81+162-32)/4#

#y=49/4#

And so the vertex is #(9/2,49/4)#