Solving Quadratics Transformations

y > -8

y < -8

x = all real numbers

y = all real numbers

(-4, 0)

cannot be determined

(-1, -9)

(0, -8)

x = 4

x = 2, 6

x = 3.2, 4.8

cannot be determined on the graph

vertical compression and shift up

reflection over x-axis, vertical compression, and shift up

reflection over x-axis, vertical stretch, and shift up

vertical stretch and shift down

compress

stretch

compress

stretch

$$e\left(x\right)=x^2\ +\ 3$$  

$$e\left(x\right)=f\left(x\right)\ +\ 3$$  

$$e\left(x\right)=x^2\ -\ 3$$  

$$e\left(x\right)=f\left(x\right)\ -\ 3$$  

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

$$e\left(x\right)=f\left(x\ -\ 3\right)$$  

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

$$e\left(x\right)=f\left(x\ +\ 3\right)$$  

$$e\left(x\right)=3f\left(x\right)$$  

$$e\left(x\right)=3x^2$$  

compress

stretch