# How do you write f(x) = −2x^2 − 4x + 7 in vertex form?

Apr 29, 2017

$f \left(x\right) = - 2 {\left(x + 1\right)}^{2} + 9$

#### Explanation:

The equation of a parabola in $\textcolor{b l u e}{\text{vertex form}}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a {\left(x - h\right)}^{2} + k} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where (h , k) are the coordinates of the vertex and a is a constant.

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

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

Since we are adding a value that is not there we must also subtract the value.

$\text{that is add/subtract } {\left(\frac{2}{2}\right)}^{2} = 1$

$- 2 \left({x}^{2} + 2 x\right) + 7 \leftarrow \text{ coefficient of " x^2" is unity}$

$= - 2 \left({x}^{2} + 2 x \textcolor{red}{+ 1} \textcolor{red}{- 1}\right) + 7$

$= - 2 {\left(x + 1\right)}^{2} + 2 + 7$

$\Rightarrow f \left(x\right) = - 2 {\left(x + 1\right)}^{2} + 9 \leftarrow \textcolor{red}{\text{ in vertex form}}$