Algebra Examples

f (x) = - {(x - 1)}^{2} + 2

$f (x) = - {(x - 1)}^{2} + 2$

Step 1

The parent function is the simplest form of the type of function given.

g (x) = x^{2}

$g (x) = x^{2}$

Step 2

The transformation being described is from

g (x) = x^{2}

$g (x) = x^{2}$ to

f (x) = - {(x - 1)}^{2} + 2

$f (x) = - {(x - 1)}^{2} + 2$ .

g (x) = x^{2} \to f (x) = - {(x - 1)}^{2} + 2

$g (x) = x^{2} \to f (x) = - {(x - 1)}^{2} + 2$

Step 3

The horizontal shift depends on the value of

h

$h$ . The horizontal shift is described as:

f (x) = f (x + h)

$f (x) = f (x + h)$ - The graph is shifted to the left

h

$h$ units.

f (x) = f (x - h)

$f (x) = f (x - h)$ - The graph is shifted to the right

h

$h$ units.

Horizontal Shift: Right

1

$1$ Units

Step 4

The vertical shift depends on the value of

k

$k$ . The vertical shift is described as:

f (x) = f (x) + k

$f (x) = f (x) + k$ - The graph is shifted up

k

$k$ units.

f (x) = f (x) - k

$f (x) = f (x) - k$ - The graph is shifted down

k

$k$ units.

Vertical Shift: Up

2

$2$ Units

Step 5

The graph is reflected about the x-axis when

f (x) = - f (x)

$f (x) = - f (x)$ .

Reflection about the x-axis: Reflected

Step 6

The graph is reflected about the y-axis when

f (x) = f (- x)

$f (x) = f (- x)$ .

Reflection about the y-axis: None

Step 7

Compressing and stretching depends on the value of

a

$a$ .

When

a

$a$ is greater than

1

$1$ : Vertically stretched

When

a

$a$ is between

0

$0$ and

1

$1$ : Vertically compressed

Vertical Compression or Stretch: None

Step 8

Compare and list the transformations.

Parent Function:

g (x) = x^{2}