# What is the vertex form of y=x^2 - 3x +4?

Jun 5, 2017

$y = {\left(x - \frac{3}{2}\right)}^{2} + \frac{7}{4}$

#### Explanation:

$\text{the equation of a parabola in vertex form is}$

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

$\text{for a parabola in standard form } y = a {x}^{2} + b x + c$

${x}_{\textcolor{red}{\text{vertex}}} = - \frac{b}{2 a}$

$y = {x}^{2} - 3 x + 4 \text{ is in this form}$

$\text{with } a = 1 , b = - 3 , c = 4$

$\Rightarrow {x}_{\textcolor{red}{\text{vertex}}} = - \frac{- 3}{2} = \frac{3}{2}$

$\text{substitute this value into function to obtain y}$

$\Rightarrow {y}_{\textcolor{red}{\text{vertex}}} = {\left(\frac{3}{2}\right)}^{2} - \left(3 \times \frac{3}{2}\right) + 4 = \frac{7}{4}$

$\Rightarrow \textcolor{m a \ge n t a}{\text{vertex }} = \left(\frac{3}{2} , \frac{7}{4}\right)$

$\Rightarrow y = {\left(x - \frac{3}{2}\right)}^{2} + \frac{7}{4} \leftarrow \textcolor{red}{\text{ in vertex form}}$