# How do you find the VERTEX of a parabola y=x^2-x-6?

Jul 21, 2015

The vertex is $\left(\frac{1}{2} - \frac{25}{4}\right)$ or $\left(\frac{1}{2} , - 6 \frac{1}{4}\right)$.

#### Explanation:

$y = {x}^{2} - x - 6$ is a quadratic equation in the form of $a {x}^{2} + {b}^{2} + 6$, where $a = 1 , b = - 1 , \mathmr{and} c = - 6$.

The vertex is the minimum or maximum point of the equation. The $x$ value can be found using the formula $x = \frac{- b}{2 a}$. The $y$ value can be found by substituting the value for $x$ into the equation and solving for $y$.

The value of $x$.

$x = \frac{- b}{2 a} = \frac{- \left(- 1\right)}{2 \cdot 1} = \frac{1}{2}$

$x = \frac{1}{2}$

The value of $y$.

$y = {\left(\frac{1}{2}\right)}^{2} - 1 \left(\frac{1}{2}\right) - 6$ =

$y = \frac{1}{4} - \frac{1}{2} - 6$ =

The common denominator for the right side is $4$. Multiply each term by a fraction so that it has a denominator of $4$.

$y = \frac{1}{4} - \frac{1}{2} \left(\frac{2}{2}\right) - 6 \left(\frac{4}{4}\right)$ =

$y = \frac{1}{4} - \frac{2}{4} - \frac{24}{4}$ =

$y = - \frac{25}{4}$

Simplify the improper fraction.

$y = - 6 \frac{1}{4}$

graph{y=x^2-x-6 [-14.24, 14.23, -7.12, 7.12]}