Question

Describe how the graph of y= x^2 can be transformed to the graph of the given equation.

y = x^2 - 12 (5 points)

a) Shift the graph of y = x2 left 12 units.
b) Shift the graph of y = x2 down 12 units.
c) Shift the graph of y = x2 right 12 units.
d) Shift the graph of y = x2 up 12 units.

Answer 1

b

Explanation:

Given y = x² then y = x² + c is a vertical translation of y = x²

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

Here c = - 12 < 0

Thus y = x² - 12 is the graph of y = x² shifted 12 units down → b

Answer 2

b) Shift the graph of y = x2 down 12 units.

Explanation:

Graphs

The graph of the function

`y=x^2`

can be found by giving the variable x some values and calculating the values of y as follows:

For x=-2,
`y=(-2)^2=4`. Point (-2,4)

For x=-1,
`y=(-1)^2=1`. Point (-1,1)

For x=0,
`y=(0)^2=0`. Point (0,0)

For x=1,
`y=(1)^2=1`. Point (1,1)

For x=2,
`y=(2)^2=4`. Point (2,4)

The graph of

`y=x^2-12`

Can be similarly found:

For x=-2,
`y=(-2)^2-12=-8`. Point (-2,-8)

For x=-1,
`y=(-1)^2-12=-11`. Point (-1,-11)

For x=0,
`y=(0)^2-12=-12`. Point (0,-12)

For x=1,
`y=(1)^2-12=-11`. Point (1,-11)

For x=2,
`y=(2)^2-12=-8`. Point (2,-8)

The graphs are shown in the attached image. It can be clearly seen that the second graph (in blue) is shifted down 12 units with respect to the red graph. Answer:

b) Shift the graph of y = x2 down 12 units.