Question

What is "vertex (2,1)​, point (1, -5)" in vertex form?

Answer 1

Also could someone show me how to write it in vertex form, please?

Answer 2

If the vertex is (h, k), then the form of the equation you want is
y = a(x - h)^2 + k , so for your information with a vertex of (2,1) you have
y = a(x - 2)^2 + 1
so the only missing part is the value of a
but you also know that the point (1, -5) lies on your parabola, so ....
-5 = a(1-2)^2 + 1
-6 = -a
a = 6

equation : y = 6(x - 2)^2 + 1

Answer 3

that should have been
a = -6
and
y = -6(x - 2)^2 + 1