Quadratic Transformations MMA

Up 1 unit

Down 1 unit

Left 1 unit

Right 1 unit

Up 2 units, left 4 units

Down 2 units, right 4 units

Right 2 units, up 4 units

Left 2 units, up 4 units

Left 5 units, up 1 unit

Right 5 units, up 1 unit

Up 5 units, right 1 unit

Down 5 units, left 1 unit

Vertical stretch by a factor of  $\frac{1}{3}$  ,right 6 units

Vertical compression by a factor of  $\frac{1}{3}$  , right 6 units

Vertical stretch by a factor of  $\frac{1}{3}$  , left 6 units

Vertical compression by a factor of  $\frac{1}{3}$  , left 6 units

Vertical stretch by a factor of 2, right 3 units, up 1 unit

Vertical compression by a factor of 2, left 3 units, down 1 unit

Vertical stretch by a factor of 2, left 3 units, down 1 unit

Vertical compression by a factor of 2, right 3 units, down 1 unit

 $f\left(x\right)=-5\left(x+3\right)^2$  

 $f\left(x\right)=-5\left(x-3\right)^2$  

 $f\left(x\right)=-3\left(x-5\right)^2$  

 $f\left(x\right)=-3\left(x+5\right)^2$  

$f\left(x\right)=\left(x-4\right)^2+3$

$f\left(x\right)=\left(x+4\right)^2+3$

$f\left(x\right)=\left(x-4\right)^2-3$

$f\left(x\right)=\left(x+4\right)^2-3$

 $y=2\left(x+\frac{1}{4}\right)^2$  

 $y=\frac{1}{4}\left(x+2\right)^2$  

 $y=2\left(x-\frac{1}{4}\right)^2$  

 $y=\frac{1}{4}\left(x-2\right)^2$  

$y=2\left(x-1\right)^2-3$

$y=2\left(x+1\right)^2+3$

$y=3\left(x-1\right)^2-2$

$y=3\left(x+1\right)^2-2$

 $f\left(x\right)=\frac{1}{2}x^2-5$  

 $f\left(x\right)=\frac{1}{2}x^2+5$  

 $f\left(x\right)=\frac{1}{2}\left(x+5\right)^2$  

 $f\left(x\right)=\frac{1}{2}\left(x-5\right)^2$