# How do you write Y=-6(x-2)^2-9 in standard form?

Oct 6, 2017

$y = - 6 {x}^{2} + 24 x - 33$

#### Explanation:

Standard form for a quadratic is $y = a {x}^{2} + b x + c$

The best way to do this is to simplify using order of operations.

First exponents,

${\left(x - 2\right)}^{2} = \left(x - 2\right) \left(x - 2\right)$
Using FOIL x*x=x^2, x*-2=-2x, -2*x=-2x, and -2*-2=4

So $\left(x - 2\right) \left(x - 2\right) = {x}^{2} - 2 x - 2 x + 4 = {x}^{2} - 4 x + 4$

Next multiplication,

$- 6 \left({x}^{2} - 4 x + 4\right) = - 6 {x}^{2} + 24 x - 24$

Finally subtraction,

$- 6 {x}^{2} + 24 x - 24 - 9 = - 6 {x}^{2} + 24 x - 33$