Question

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

Answer 1

$y = -2(x-5)^2 + 7$

That's vertex form for a parabola $y=a(x-p)^2+q$ and we read off vertex (p,q) as

Answer: Vertex (5,7)

The negative a tells us this is a downward opening parabola (upside down from the usual $y=x^2$. 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.

Answer: downward