# Quadratic Graphs by Completing the Square

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

### 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.

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