# What is the vertex of y=x^2-2x+1+(x-3)^2 ?

Apr 11, 2018

$\left(2 , 2\right)$

#### Explanation:

Let's simplify the expression,

$\text{ } y = {x}^{2} - 2 x + 1 + {x}^{2} + 9 - 6 x$

$\implies \text{ } y = 2 {x}^{2} - 8 x + 10$

$\implies \text{ } \frac{y}{2} - 1 = {x}^{2} - 4 x + 4$

$\implies \text{ } \frac{1}{2} \left(y - 2\right) = {\left(x - 2\right)}^{2}$

This is the equation of standard parabola of the form ${x}^{2} = 4 a y$

The origin is shifted and so the new vertex is $\left(2 , 2\right)$