Question

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

Answer 1

Translation of `y=x^2`

Explanation:

When a quadratic is in the form `y=(x-p)^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 `(-p, q)`

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

`((9),(5))`