Question 478335
Find the vertex f(x) = -2x^2+2x+6
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Standard form of an equation for a parabola: A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex. A is a multiplier which affects the steepness of the curve.
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f(x)=-2x^2+2x+6
completing the square to see equation in standard form
f(x)=-2(x^2-x+1/4)+6+1/2
f(x)=-2(x-1/2)^2+13/2
This is an equation of a parabola with vertex at (1,13/2). The negative coefficient of the lead term means it opens downward, that is, it has a maximum.
see the graph below as a visual check on the answer
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{{{ graph( 300, 300, -10, 10, -10, 10,-2x^2+2x+6) }}}