# What is y=2(x+3)^2+1 in standard form?

Mar 1, 2016

$y = 2 {\left(x + 3\right)}^{2} + 1$ in standard form is $\textcolor{p u r p \le}{y = 2 {x}^{2} + 12 x + 19}$.

#### Explanation:

$y = 2 {\left(x + 3\right)}^{2} + 1$ is a quadratic equation in vertex form. It can be converted into standard form by doing the following:

Remove the parentheses and exponent by simplifying ${\left(x + 3\right)}^{2}$, which is a sum of squares.

${a}^{2} + {b}^{2} = {a}^{2} + 2 a b + {b}^{2}$, where $a = x , \mathmr{and} b = 3$.

$\textcolor{b l u e}{{\left(x + 3\right)}^{2} = {x}^{2} + 2 \cdot x \cdot 3 + {3}^{2}}$

Simplify.

color(blue)((x^2+6x+9)

Rewrite the equation, substituting $\textcolor{b l u e}{\left({x}^{2} + 6 x + 9\right)}$ for ${\left(x + 3\right)}^{2}$.

$y = 2 \textcolor{b l u e}{\left({x}^{2} + 6 x + 9\right)} + 1$

Distribute the $\textcolor{red}{2}$.

$y = \textcolor{red}{2} \cdot {x}^{2} + 6 x \cdot \textcolor{red}{2} + 9 \cdot \textcolor{red}{2} + 1$

Simplify.

$y = \textcolor{p u r p \le}{2 {x}^{2} + 12 x + 18} + 1$

Simplify.

$\textcolor{p u r p \le}{y = 2 {x}^{2} + 12 x + 19}$