Quadratic Graphs in Completed Square Form

$$y=(x-a)^2+b$$

Example 1

Draw the graph of $y=(x-1)^2+2$.

The vertex is $(1,2)$ and the graph is concave up.

Example 2

Draw the graph of $y=(x-1)^2-2$.

The vertex is $(1,-2)$ and the graph is concave up.

Example 3

Draw the graph of $y=(x+1)^2+2$.

The vertex is $(-1,2)$ and the graph is concave up.

Example 4

Draw the graph of $y=(x+1)^2-2$.

The vertex is $(-1,-2)$ and the graph is concave up.

Example 5

Draw the graph of $y=-(x-1)^2+2$.

The vertex is $(1,2)$ and the graph is concave down.

Example 6

Draw the graph of $y=-(x-1)^2-2$.

The vertex is $(1,-2)$ and the graph is concave down.

Example 7

Draw the graph of $y=-(x+1)^2+2$.

The vertex is $(-1,2)$ and the graph is concave down.

Example 8

Draw the graph of $y=-(x+1)^2-2$.

The vertex is $(-1,2)$ and the graph is concave down.