Concave up for $a \gt 0$

Concave down for $a \lt 0$

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

Concave up for $a \gt 0$

Concave down for $a \lt 0$

### 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 $y=-(x+1)^2-2$.

Concave up for $a \gt 0$

Concave down for $a \lt 0$

$y=x^2$ is translated to the right $\rightarrow$ by $1$ unit and up $\uparrow$ by $2$ units.

$y=x^2$ is translated to the right $\rightarrow$ by $1$ unit and down $\downarrow$ by $2$ units.

$y=x^2$ is translated to the left $\leftarrow$ by $1$ unit and up $\uparrow$ by $2$ units.

$y=x^2$ is translated to the left $\leftarrow$ by $1$ unit and down $\downarrow$ by $2$ units.

$y=-x^2$ is translated to the right $\rightarrow$ by $1$ unit and up $\uparrow$ by $2$ units.

$y=-x^2$ is translated to the right $\rightarrow$ by $1$ unit and down $\downarrow$ by $2$ units.

$y=-x^2$ is translated to the left $\leftarrow$ by $1$ unit and up $\uparrow$ by $2$ units.

$y=-x^2$ is translated to the left $\leftarrow$ by $1$ unit and down $\downarrow$ by $2$ units.