# What is the vertex form of y= 3x^2-10x-14?

May 29, 2017

$y = 3 {\left(x - \frac{5}{3}\right)}^{2} - \frac{67}{3}$

#### Explanation:

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

color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|))
where ( h , k ) are the coordinates of the vertex and a is a constant.

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

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

$y = 3 {x}^{2} - 10 x - 14 \text{ is in this form}$

$\text{with } a = 3 , b = - 10 , c = - 14$

$\Rightarrow {x}_{\textcolor{red}{\text{vertex}}} = - \frac{- 10}{6} = \frac{5}{3}$

$\text{for y-coordinate, substitute this value into the equation}$

$\Rightarrow {y}_{\textcolor{red}{\text{vertex}}} = 3 {\left(\frac{5}{3}\right)}^{2} - 10 \left(\frac{5}{3}\right) - 14 = - \frac{67}{3}$

$\Rightarrow \textcolor{m a \ge n t a}{\text{vertex }} = \left(\frac{5}{3} , - \frac{67}{3}\right)$

$\Rightarrow y = 3 {\left(x - \frac{5}{3}\right)}^{2} - \frac{67}{3} \leftarrow \textcolor{red}{\text{ in vertex form}}$