# What is the domain and range of the quadratic equation y = (x – 5)^2 + 10?

$\mathbb{R}$
$\left[10 , + \infty\right)$
The domain is obviously $\mathbb{R}$ since it is well defined everywhere. Since for all the vapes of $x$ the factor ${\left(x - 5\right)}^{2}$ is always positive and zero if $x = 5$, the range of the quadratic equation goes from the image of the minimum ($y \left(5\right) = 10$) to infinity, so it is $\left[10 , + \infty\right)$