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What is the axis of symmetry and vertex for the graph #F(x) = x ^ 2 - 4x - 5#?

Answer 1

Julia Adams

This is not a conventional way to derive the answer. It uses part of the process for 'completing the square'.

Vertex #->(x,y)=(2,-9)#
Axis of symmetry #->x=2#

Consider the standard form of #y=ax^2+bx+c#

Write as :#y=a(x^2+b/a x) +c#

#x_("vertex")="axis of symmetry" = (-1/2)xxb/a#

The the context of this question #a=1#

#x_("vertex")="axis of symmetry" = (-1/2)xx(-4)/1 = +2#

So by substitution

#y_("vertex")=(2)^2-4(2)-5 = -9#

Thus we have:

Vertex #->(x,y)=(2,-9)#
Axis of symmetry #->x=2#

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Answer 2

Abigail Allen

The axis of symmetry for the graph of ( F(x) = x^2 - 4x - 5 ) is ( x = 2 ), and the vertex is at ( (2, -9) ).

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