# What is the vertex of  y= x^2- 6x + 14 ?

Jan 31, 2016

(3, 5)

#### Explanation:

The x-coordinate of the vertex of a parabola is given by $- \frac{b}{2 a}$. Remember that parabolas in standard form are $a {x}^{2} + b x + c$. With this in mind, we can see that, for our parabola, $a = 1$, $b = - 6$, and $c = 14$.

To find the x-coordinate of the vertex, we just plug in the value of $a$ and $b$ into $- \frac{b}{2 a}$:

Vertex = $- \frac{- 6}{2 \left(1\right)} = \frac{6}{2} = 3$

Now that we have the $x$, we plug it into our parabola to find $y$:

${\left(3\right)}^{2} - 6 \left(3\right) + 14 = 9 - 18 + 14 = 5$

Our y-coordinate is 5, meaning our vertex is the point (3,5).