Question 131896
To find the x-coordinate of the vertex, we can use this formula:

{{{x=-b/(2a)}}}

From the equation {{{f(x)=-2x^2+2x+6}}} we can see that a=-2 and b=2

{{{x=(-2)/(2*-2)}}} Plug in b=2 and a=-2

{{{x=(-2)/-4}}} Multiply 2 and -2 to get -4

{{{x=1/2}}} Reduce

So the  x-coordinate of the vertex is  {{{x=1/2}}}.

This also means that the line of symmetry is {{{x=1/2}}}.

Now lets plug this into the equation to find the y-coordinate of the vertex.

Lets evaluate {{{f(1/2)}}}

{{{f(1/2)=-2(1/2)^2+2(1/2)+6}}} Plug in {{{x=1/2}}}

{{{f(1/2)=-2(1/4)+2(1/2)+6}}} Square {{{1/2}}} to get {{{1/4}}}

{{{f(1/2)=-1/2+2(1/2)+6}}} Multiply -2 by {{{1/4}}} to get {{{-1/2}}}

{{{f(1/2)=-1/2+1+6}}} Multiply 2 by {{{1/2}}} to get 1

{{{f(1/2)=13/2}}} Combine like terms

So the vertex is *[Tex \LARGE \left(\frac{1}{2},\frac{13}{2}\right)]

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