[latex]y=-2x^2+6x+5\ a=-2\ p=frac{-b}{2a}=frac{-6}{-4}=1,5\ q=-2(1,5)^2+6cdot1,5+5=-4,5+9+5=9,5\\ oxed{y=-2(x-1,5)^2+9,5}[/latex]

[latex]\p=- dfrac{b}{2a} , q=- dfrac{Delta}{4a} \ \ \p= dfrac{-6}{-4} = dfrac{3}{2} \ \ \Delta=6^2+4cdot2cdot5=36+40=76 \ \q=- dfrac{76}{-8} = dfrac{19}{2} \ \ \f(x)=-2(x- frac{3}{2} )^2+ frac{19}{2} [/latex]