Answer
vertical parabola: Choices A and D
horizontal parabola: Choices B and C
Work Step by Step
A vertical parabola has an equation with an $x^2$ variable, while a horizontal parabola has a $y^2$ variable.
Hence, $y=-x^2+20x+80$ (Choice A) and $f(x)=(x-4)^2$ (Choice D) are vertical parabolas, while $x=2y^2+6y+5$ (Choice B) and $x+1=(y+2)^2$ (Choice C) are horizontal parabolas.