# Quadratic Graphs by Completing the Square $y=(x-a)^2+b$

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

$$y=(x-a)^2+b$$ ### Example 1

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

Draw the graph of $y=(x-1)^2-2$. ### Example 3

Draw the graph of $y=(x+1)^2+2$. ### Example 4

Draw the graph of $y=(x+1)^2-2$. ### Example 5

Draw the graph of $y=-(x-1)^2+2$. ### Example 6

Draw the graph of $y=-(x-1)^2-2$. ### Example 7

Draw the graph of $y=-(x+1)^2+2$. ### Example 8

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

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

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

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

The vertex is $(-1,-2)$ and the graph is concave up. \end{align} \)

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

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

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

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