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

Jun 17, 2018

The vertex is at $\left(\frac{1}{6} , - 3 \frac{1}{2}\right)$ or about $\left(0.167 , - 3.083\right)$.

#### Explanation:

$y = 3 {x}^{2} - x - 3$

The equation is a quadratic equation in standard form, or $y = \textcolor{red}{a} {x}^{2} + \textcolor{g r e e n}{b} x + \textcolor{b l u e}{c}$.

The vertex is the minimum or maximum point of a parabola . To find the $x$ value of the vertex, we use the formula ${x}_{v} = - \frac{\textcolor{g r e e n}{b}}{2 \textcolor{red}{a}}$, where ${x}_{v}$ is the x-value of the vertex.

We know that $\textcolor{red}{a = 3}$ and $\textcolor{g r e e n}{b = - 1}$, so we can plug them into the formula:
${x}_{v} = \frac{- \left(- 1\right)}{2 \left(3\right)} = \frac{1}{6}$

To find the $y$-value, we just plug in the $x$ value back into the equation:
$y = 3 {\left(\frac{1}{6}\right)}^{2} - \left(\frac{1}{6}\right) - 3$

Simplify:
$y = 3 \left(\frac{1}{36}\right) - \frac{1}{6} - 3$

$y = \frac{1}{12} - 3 \frac{1}{6}$

$y = \frac{1}{12} - 3 \frac{2}{12}$

$y = - 3 \frac{1}{12}$

Therefore, the vertex is at $\left(\frac{1}{6} , - 3 \frac{1}{2}\right)$ or about $\left(0.167 , - 3.083\right)$.

Here is a graph of this quadratic equation:

As you can see, the vertex is at $\left(0.167 , - 3.083\right)$.

For another explanation/example of finding the vertex and intercepts of a standard equation, feel free to watch this video:

Hope this helps!