y=-2(x-5)^2+7
y=-2(x^2-10x+25)+7
y=-2x^2+20x-50+7
y=-2x^2+20x-43
dy/dx=-4x+20, d2y/dx2=-4
Since acceleration, d2y/dx2 is a constant negative, when dy/dx, velocity, equals zero, it represent the absolute maximum for y...
dy/dx=0 only when 4x=20, x=5
y(5)=7 so the vertex is at the point (5, 7). It has an absolute maximum at that point and decreases without bound on either side of x=5. So the parabola opens downward.
