How do I use the vertex formula to determine the vertex of the graph of the function and write it in standard form for f(x)=x^2-10x?

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Answer 1 · 2015-05-17T20:40:14

The vertex formula for a quadratic equation #a x^2 + b x + c# #=# 0 is the following:

#x_v# = #- b / (2 a)# and #y_v# = #- Delta / (4 a)#, where #Delta = b^2 - 4 a c#

In other words, the vertex is the point #V# #(- b / (2 a)#; #- Delta / (4 a))#

in our particular case #(y = x^2 - 10 x)#, the coordinates of the vertex will be:

#x_v = - (-10)/2##=# #5#

#y_v = -(100/4)##=##-25#

Therefore, the vertex is the point #V##(5; -25)#