Question

why is the vertex of a parabola having the equation y= -2 (x -5)2 + 7 which direction does the parabola open

Answer 1

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.