It's a parabola with a vertex at (0,-3) that also passes through (2,1)
In general we have vertex (p,q) and scale factor a giving parabola
y = a(x - p)² + q
We know (p,q)=(0,-3) so we put in (x,y)=(2,1) and solve for a:
1 = a(2 - 0)² + -3
1 = 4a - 3
4 = 4a
a = 1
So our equation is
y = x² - 3
which is both vertex form and standard form.
Answer: vertex form: y = x² - 3 standard form: y = x² - 3
