Aparabola has a vertex at (0, –1) and passes through the point (2, 2). which of the following is the equation of this parabola in the form

For vertex at (h,k)
the equation is
y=a(x-h)^2+k

for vertex at (0,-1)
equation is
y=a(x-0)^2+(-1) or
y=ax^2-1
find what a is

(2,2)
x=2
y=2
2=a(2^2)-1
2=a(4)-1
add 1
3=a(4)
divide both sides by 4
3/4=a

the equation is
y=3/4x^2-1