How do you find the vertex of y = x^2 - 6x + 7?

Apr 14, 2018

$\left(3 , - 2\right)$

Explanation:

The equation is in standard form: $y = a {x}^{2} + b x + c$

Finding the vertex of an equation in standard form: $\left(\frac{- b}{2 a} , f \left(\frac{- b}{2 a}\right)\right)$

Here, $a$ is $1$ and $b$ is $- 6$

$\frac{- \left(- 6\right)}{2 \cdot 1}$

$\frac{6}{2}$

$3 \rightarrow$ The x-coordinate of the vertex is $3$.

$f \left(3\right) = {3}^{2} - 6 \cdot 3 + 7$

$f \left(3\right) = 9 - 6 \cdot 3 + 7$

$f \left(3\right) = 9 - 18 + 7$

$f \left(3\right) = - 9 + 7$

$f \left(3\right) = - 2$