Identifying Vertex Form

(-2,4)

(-1,1)

(0,0)

(2,4)

(-1,-9)

(0,-8)

(-4,0)

(0,0)

( 6 , -2 )

( 1 , -2 )

( 0 , -2 )

( -2 , 0 )

a=-1, h=3, k=2

a=3, h=3, k=3

a=1, h=-3, k=2

a=1, h=-3, k=-2

$$y=ax^2+bx+c$$

$$y=a\left(x-p\right)\left(x-q\right)$$

$$y=a\left(x-h\right)^2+k$$

the y-intercept

the x-intercepts

the vertex

the increasing interval

$$y=ax^2+bx+c$$  

$$y=a\left(x-p\right)\left(x-q\right)$$  

$$y=a\left(x-h\right)^2+k$$  

$$y=mx+b$$  

opens up/down

vertical stretch/compress

horizontal shift

vertical shift

horizontal stretch/compress

vertical flip

horizontal flip

vertical stretch

horizontal compression

reflection across y-axis

x = -b/2a

x = (-b ±√b² - 4ac)/2a

y = ax² + bx + c

y = a(x - h)² + k