Question

What is the standard form of `y-4= -(x-1)^2`?

Answer 1

`y=-x^2+2x-3`

Explanation:

The standard form is
`y=ax^2 +bx +c`
(where `a`, `b` and `c` are some numbers)
So in this case, you just need to open up the parentheses of the right side of the equation and then rearrange the terms.

We have:
`y-4 = -(x-1)^2`
which becomes:
`y-4=-(x^2-2x+1)`
(note that I still keep the minus sign in front of the parenthesis)

`y-4=-x^2+2x-1`

And pass the -4 on the "other side":
`y=-x^2+2x-1+4`

giving you:
`y=-x^2+2x-3`
which is in standard form with
`a=-1`, `b=2` and `c=-3`