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

##### 1 Answer
Nov 16, 2017

$V e r t e x \left(\frac{3}{4} , - \frac{15}{4}\right)$

#### Explanation:

In this form of the Parabola equation, i.e.:

$a {x}^{2} + b x + c$

the vertex has coordinates of:

$x = - \frac{b}{2 a}$ and $y = f \left(- \frac{b}{2 a}\right)$

In this problem:

$a = \frac{4}{3}$ and $b = - 2$ and $c = - 3$

$x$-coordinate of the vertex =$\frac{- \left(- 2\right)}{2 \left(\frac{4}{3}\right)} = \frac{2}{\frac{8}{3}} = 2 \cdot \left(\frac{3}{8}\right) = \frac{3}{4}$

$y$-coordinate of the vertex can be found by plugging in the value of the $x$-coordinate into the equation of the Parabola.

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

$y = \left(\frac{4}{3}\right) \left(\frac{9}{16}\right) - \left(\frac{3}{2}\right) - 3$

$y = \frac{3}{4} - \frac{3}{2} - 3$

$y = \frac{3 - 6 - 12}{4} = - \frac{15}{4}$