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

Nov 29, 2015

$y = - {x}^{2} + 2 x - 3$

#### Explanation:

The standard form is
$y = a {x}^{2} + b x + c$
(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:
$y - 4 = - {\left(x - 1\right)}^{2}$
which becomes:
$y - 4 = - \left({x}^{2} - 2 x + 1\right)$
(note that I still keep the minus sign in front of the parenthesis)

$y - 4 = - {x}^{2} + 2 x - 1$

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

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