# How do you sketch the graph of y=(x-9)^2+5 and describe the transformation?

Jul 8, 2017

Translation of $y = {x}^{2}$

#### Explanation:

When a quadratic is in the form $y = {\left(x - p\right)}^{2} + q$ such as this, the negative of $p$ tells us the $x$ coordinate of the vertex of the graph and $q$ tells us the $y$ coordinate.

ie vertex is $\left(- p , q\right)$

Consider the graph $y = {x}^{2}$ and you will notice that it has shifted (translation) $9$ units to the right $- \left(- 9\right) \mathmr{and} 5$ units up. We often write this in column vector form:

$\left(\begin{matrix}9 \\ 5\end{matrix}\right)$