What is the axis of symmetry and vertex for the graph #f(x) = -x^2 +14x +5 #?

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Answer 1 · 2018-04-07T02:49:21

Axis of symmetry: #x=7# Vertex: #(7, 54)#

The axis of symmetry is the #x-#coordinate of the vertex, a vertical line across which the graph exhibits symmetry, given by

#x=-b/(2a)# when the quadratic is in the form #ax^2+bc+c#

Here, we see #b=14, a=-1#; thus, the axis is

#x=-14/(2*-1)=-14/-2=7#

The coordinates of the vertex are given by #(-b/(2a), f(-b/(2a))#. We know #-b/(2a)=7,# so we need #f(7).#

#f(7)=-7^2+14(7)+5=-49+98+5=54#

The vertex is then

#(7, 54)#