Quadratic Graph of $y=a(x-b)^2+c$ Form

$$y=a(x-b)^2+c$$ Vertex $(b,c)$
Concave up for $a \gt 0$
parabola concave up
Concave down for $a \lt 0$
parabola concave down

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