# How do you write the function in standard form y=-(9x+2)^2+4x?

Nov 11, 2017

To put equations in standard form we must reorganize them from highest to lowest power.

#### Explanation:

$\left(9 x + 2\right) \left(9 x + 2\right) = 81 {x}^{2} + 36 + 4$

$y = - \left(81 {x}^{2} + 36 x + 4\right) + 4 x$

distribute the negative to the parentheses

$y = - 81 {x}^{2} \textcolor{red}{- 36 x} - 4 + \textcolor{red}{4 x}$

$y = - 81 {x}^{2} - 32 x - 4$

as you can see this a quadtratic function so our $y = 0$ because a quadratic equation gives us the $x$ values.

$0 = - 81 {x}^{2} - 32 x - 4$

add everything to the $0$ making terms positive (which is required for standard form)

$81 {x}^{2} + 32 x + 4 = 0$

as you can see it is now it is in order of highest powers to lowest and in standard form