What is the axis of symmetry and vertex for the graph #f(x)=x^2-2x-6#?

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Answer 1 · 2017-06-02T00:42:43

#"axis of symmetry" => x=1#

#"vertex" => (1,-7)#

For a parabola #f(x)=ax^2+bx+c#, the axis of symmetry is given by: #x = -b/(2a#.

Also, the vertex is given by #((-b)/(2a), f((-b)/(2a)))# since it lies on the axis of symmetry.

Therefore, our axis of symmetry for this graph is given by:

#x=-b/(2a) = -(-2)/(2(1)) = 1#

And the vertex is therefore given by #(1, f(1))#.

#f(1) = 1^2-2(1)-6#

#f(1) = 1-2-6 = -7#

So the vertex is #(1,-7)#

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