Characteristics of Quadratic Functions

$$f\left(x\right)=-x^2+5$$  

$$f\left(x\right)=\frac{1}{2}x^2-3x+10$$  

$$f\left(x\right)=6x^2$$  

$$f\left(x\right)=-2x^2-15x\ +1$$  

$$f\left(x\right)=-\frac{2}{3}x^2+5x-7$$  

Vertical stretch by a factor of 1/3.

Vertical shrink by a factor of 1/3.

Vertical translation up 1/3 units.

Reflection across the x-axis.

$$f\left(x\right)=\frac{1}{6}x^2$$  

$$g\left(x\right)=-\frac{1}{4}x^2$$  

$$j\left(x\right)=3x^2$$  

$$h\left(x\right)=-5x^2$$  

Vertical shrink by a factor of 5.

Vertical stretch by a factor of 5.

Vertical translation 5 units up.

Vertical translation 5 units down.

$$x\ge-3$$  

$$x\le-3$$  

all real numbers

cannot tell by just looking at the equation.

$$y\ge2$$  

$$y\ge4$$  

$$y\le4$$  

$$y\le2$$  

$$y\ge-5$$  

All real numbers

cannot determine from the equation

$$y\le-5$$  

True

False

x = 2

x = -2

x = 4

x = -4

$$g\left(x\right)=6x^2-5$$  

$$h\left(x\right)=\frac{2}{5}x^2+4$$  

$$i\left(x\right)=\frac{1}{3}x^2-9$$  

$$j\left(x\right)=3x^2+9$$