open up or down, vertex:(0,-4), passes through: (-3,5)
In this problem we have a vertical parabola open upward
the equation in vertex form is equal to
y=a(x-h)^2+k
where (h,k) is the vertex
we have
(h,k)=(0,-4)
substitute
y=a(x)^2-4
Find the value of a
with the point (-3,5)
substitute in the equation
5=a(-3)^2-4
5=9a-4
9a=5+4
9a=9
a=1
therefore
the equation is
y=x^2-4
answer is
f(x)=x^2-4