# How do you write  y=-2(x+1)^2 +3 in standard form?

Jul 28, 2016

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

#### Explanation:

Consider $\text{ } {\left(x + 1\right)}^{2}$

Write as:$\text{ } \textcolor{b l u e}{\left(x + 1\right)} \textcolor{b r o w n}{\left(x + 1\right)}$

Multiply everything inside the right hand side bracket by everything inside the left hand bracket.

$\textcolor{b r o w n}{\textcolor{b l u e}{x} \left(x + 1\right) \textcolor{b l u e}{+ 1} \left(x + 1\right)}$

${x}^{2} + x \text{ "+x+1" "->" } {x}^{2} + 2 x + 1$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\implies \textcolor{b r o w n}{y = - 2 {\left(x + 1\right)}^{2} + 3} \textcolor{g r e e n}{\text{ "->" } y = - 2 \left({x}^{2} + 2 x + 1\right) + 3}$

$\implies y = - 2 {x}^{2} - 4 x - 2 + 3$

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