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

Apr 29, 2018

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

#### Explanation:

$y = - 6 {\left(x - 2\right)}^{2} - 9$

To write an equation in standard form, it has be in the form $y = a {x}^{2} + b x + c$. To get this, let's distribute and simplify.

$y = - 6 \left(x - 2\right) \left(x - 2\right) - 9$

Expand $\left(x - 2\right) \left(x - 2\right)$
$y = - 6 \left({x}^{2} - 2 x - 2 x + 4\right) - 9$

Combine like terms:
$y = - 6 \left({x}^{2} - 4 x + 4\right) - 9$

Multiply out the $- 6$:
$y = - 6 {x}^{2} + 24 x - 24 - 9$

Combine like terms:
$y = - 6 {x}^{2} + 24 x - 33$

Hope this helps!