# How do you write f(x) = x^2+3x-4 in vertex form?

Oct 9, 2017

$f \left(x\right) = {\left(x + \frac{3}{2}\right)}^{2} - \frac{25}{4}$

#### Explanation:

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

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

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

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

• " ensure the coefficient of the "x^2" term is 1"

• " add/subtract "(1/2"coefficient of x-term")^2" to "x^2+3x

$f \left(x\right) = {x}^{2} + 3 x - 4 \leftarrow \text{ coefficient of "x^2" term is 1}$

$\textcolor{w h i t e}{f \left(x\right)} = {x}^{2} + 2 \left(\frac{3}{2}\right) x \textcolor{red}{+ \frac{9}{4}} \textcolor{red}{- \frac{9}{4}} - 4$

$\textcolor{w h i t e}{f \left(x\right)} = {\left(x + \frac{3}{2}\right)}^{2} - \frac{25}{4} \leftarrow \textcolor{red}{\text{ in vertex form}}$