# How do you write the vertex form equation of the parabola 2x² - 4x + y + 5 = 0?

Oct 11, 2017

$y = - 2 {\left(x - 1\right)}^{2} - 3$

#### Explanation:

$\text{rearrange the equation making y the subject}$

$\Rightarrow y = - 2 {x}^{2} + 4 x - 5$

$\text{the equation of the parabola in "color(blue)"vertex form}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a {\left(x - h\right)}^{2} + k} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where "(h,k)" are the coordinates of the vertex and a}$
$\text{is a multiplier}$

$\text{to express "y=-2x^2+4x-5" in this form}$

$\text{use the method of "color(blue)"completing the square}$

• " the coefficient of the "x^2" term must be 1"

$\Rightarrow y = - 2 \left({x}^{2} - 2 x\right) - 5$

• " add/subtract "(1/2"coefficient of x-term")^2" to "x^2-2x

$y = - 2 \left({x}^{2} + 2 \left(- 1\right) x \textcolor{red}{+ 1} \textcolor{red}{- 1}\right) - 5$

$\textcolor{w h i t e}{y} = - 2 {\left(x - 1\right)}^{2} + 2 - 5$

$\Rightarrow y = - 2 {\left(x - 1\right)}^{2} - 3 \leftarrow \textcolor{red}{\text{ in vertex form}}$