# How do you write f(x)=-3x^2+24x-51 in vertex form?

##### 1 Answer
Sep 10, 2017

$f \left(x\right) = - 3 {\left(x - 4\right)}^{2} - 3$

#### Explanation:

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

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

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

• " coefficient of "x^2" term must be unity"

• " add/subtract "(1/2"coefficient of x-term")^2" to "x^2-8x

$f \left(x\right) = - 3 \left({x}^{2} - 8 x + 17\right)$

$\textcolor{w h i t e}{f \left(x\right)} = - 3 \left({x}^{2} - 8 x \textcolor{red}{+ 16} \textcolor{red}{- 16} + 17\right)$

$\textcolor{w h i t e}{f \left(x\right)} = - 3 {\left(x - 4\right)}^{2} - 3 \leftarrow \textcolor{red}{\text{ in vertex form}}$