Smith

Constant

Identity

Absolute Value

Quadratic

f(x) = |x|

f(x) = x^2

f(x) = -x

f(x) = x + 1

$$\left(-12,\ 4\right);\ \left(-6,\ 1\right);\ \left(0,\ 4\right)$$

$$\left(-9,\ 4\right);\ \left(-3,\ 1\right);\ \left(3,\ 4\right)$$

$$\left(0,\ 7\right);\ \left(3,\ 1\right);\ \left(6,\ 7\right)$$

$$\left(-6,\ 7\right);\ \left(-3,\ 1\right);\ \left(0,\ 7\right)$$

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

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

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

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

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

Translation

Reflection

Rotation

Jones

Constant

Identity

Absolute Value

Quadratic

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

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

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

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

Left 3

Right 3

Up 2

Down 2

To teach basic arithmetic

To demonstrate absolute value transformations

To simulate geometric shapes

To solve algebraic equations

Left 5

Right 5

Up 5

Down 5

g(x)=f(x)-5

g(x)=f(x)+5

g(x)=f(x-5)

g(x)=f(x+5)

vertical stretch by a factor of 2 and reflection across the x-axis

horizontal stretch by a factor of 4

horizontal translation left 1 unit

vertical translation down 3 units

Study the lesson

Play games

Watch TV

Go out with friends

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

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

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

$$f\left(x\right)=\left|x+3\right|+5$$

Science, Technology, Engineering, Math

Science, Technology, English, Math

Science, Technology, Engineering, Medicine

Science, Technology, Engineering, Management

Vertex moves 5 up

Vertex moves 3 down

Vertex moves 3 to the right

Stretched by a factor of 3

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

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

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

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