Question

Which equation is y=3(x-2)^2-(x-5)^2 rewritten in vertex form?

Answer 1

that answer is totally incomplete

Answer 2

The question does not present the options, but this does not interfere with the resolution

we have that
y=3(x-2)²-(x-5)²
y=3(x²-4x+4)-(x²-10x+25)
y=3x²-12x+12-x²+10x-25
y=(3x²-x²)+(-12x+10x)+(12-25)
y=2x²-2x-13
y+13=2x²-2x
y+13=2(x²-x)
y+13+0.50=2(x²-x+0.25)
y+13.50=2(x-0.5)²------> this is the equation in the vertex form

the vertex is the point (0.5,-13.50)