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

That's vertex form for a parabola and we read off vertex (p,q) as

Vertex (5,7)

The negative a tells us this is a downward opening parabola (upside down from the usual . I remember CUP - Concave Up Positive; here a is negative so not a cup, instead concave down. The same rule applies to second derivatives in calculus so memorize it now and use it later.

downward