Question 310556
Do you mean vertex? 
Midpoint is more of a linear term. 
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Complete the square to put the equation into vertex form. 
{{{y=-2x^2+20x+1}}}
{{{y=-2(x^2-10x+25)+1+50}}}
{{{y=-2(x-5)^2+51}}}
Vertex is (5,51)
{{{drawing( 300,300, -2, 12, -2, 58, grid(1),circle(5,51,.4),graph( 300,300, -2, 12, -2, 58, -2x^2+20x+1)) }}}