Question

f(x) g(x) ​ =x 2 =x 2 −8 ​ We can think of ggg as a translated (shifted) version of fff. Complete the description of the transformation. Use nonnegative numbers. To get the function ggg, shift fff by units.

Answer 1

Answer:

Step-by-step explanation:

The equation that results from translating the parabola y=x^2y=x

2

y, equals, x, squared to the right by \greenD{h}hstart color #1fab54, h, end color #1fab54 units and up by \goldE{k}kstart color #a75a05, k, end color #a75a05 units is:

y=(x-\greenD{h})^2+\goldE{k}y=(x−h)

2

+ky, equals, left parenthesis, x, minus, start color #1fab54, h, end color #1fab54, right parenthesis, squared, plus, start color #a75a05, k, end color #a75a05

Note that negative values of \greenD{h}hstart color #1fab54, h, end color #1fab54 represent leftward shifts and negative values for \goldE{k}kstart color #a75a05, k, end color #a75a05 represent downward shifts.

Hint #22 / 3

g(x)=(x-\greenD{0})^2+\goldE{(-8)}g(x)=(x−0)

2

+(−8)g, left parenthesis, x, right parenthesis, equals, left parenthesis, x, minus, start color #1fab54, 0, end color #1fab54, right parenthesis, squared, plus, start color #a75a05, left parenthesis, minus, 8, right parenthesis, end color #a75a05

Since the function is translated up by \goldE{-8}−8start color #a75a05, minus, 8, end color #a75a05, that means it is translated down by 888 units.

Hint #33 / 3

To get the function g, shift f down by 8 units.