# What is the vertex form of y=3x^2 -7x+5?

Jun 26, 2018

$y = 3 {\left(x - \frac{7}{6}\right)}^{2} + \frac{11}{12}$

#### Explanation:

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

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

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

$\text{to obtain this form "color(blue)"complete the square}$

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

$\text{factor out 3}$

$y = 3 \left({x}^{2} - \frac{7}{3} x + \frac{5}{3}\right)$

• " add/subtract "(1/2"coefficient of x-term")^2" to"#
${x}^{2} - \frac{7}{3} x$

$y = 3 \left({x}^{2} + 2 \left(- \frac{7}{6}\right) x \textcolor{red}{+ \frac{49}{36}} \textcolor{red}{- \frac{49}{36}} + \frac{5}{3}\right)$

$\textcolor{w h i t e}{y} = 3 {\left(x - \frac{7}{6}\right)}^{2} + 3 \left(- \frac{49}{36} + \frac{5}{3}\right)$

$\textcolor{w h i t e}{y} = 3 {\left(x - \frac{7}{6}\right)}^{2} + \frac{11}{12} \leftarrow \textcolor{red}{\text{in vertex form}}$