# How do you write y = 4(x-1)^2-10 into standard form?

May 1, 2015

Multiply it out and simplify (combine like terms) putting the terms in decreasing order of exponents.

$y = 4 {\left(x - 1\right)}^{2} - 10$
For the order of operations, we need to square before we multiply by $4$

If you need to work out ${\left(x - 1\right)}^{2}$ in the margin, or on extra paper, do so.
${\left(x - 1\right)}^{2} = \left(x - 1\right) \left(x - 1\right) = {x}^{2} - x - x + 1 = {x}^{2} - 2 x + 1$

$y = 4 {\left(x - 1\right)}^{2} - 10$

$y = 4 \left({x}^{2} - 2 x + 1\right) - 10$

$y = 4 {x}^{2} - 8 x + 4 - 10$

$y = 4 {x}^{2} - 8 x - 6$

And that's it. We are finished.