Question

The graph of g(x) is f(x) translated to the left 8 units and up 2 units. What is the function rule for g(x) given f(x)=x^2

Please show steps. Thank you! Will give a medal to best answer.

Answer 1

f(x) = A ( Bx + C ) + D

C = horizontal shift, C > 0, to the left, C < 0, to the right
D = vertical shift, D > 0, up, D < 0, down

Answer 2

so, what do you think our C and D will be?

Answer 3

I'm not sure at all how to figure these types of problems out.

Answer 4

notice
f(x) = A ( Bx + C ) + D

C = horizontal shift, C > 0, to the left, C < 0, to the right
D = vertical shift, D > 0, up, D < 0, down

our C and D components are all we need :)

Answer 5

---> translated to the left 8 units and up 2 units <----

Answer 6

C>8
D>2

Answer 7

if it's translated/shifted, to the left, that is horizontal shift, that means C >0, or positive
so +8

if it's shifted up, by 2 units, that means D > 0, or positive, that means +2

our "parent function" is \(\bf x^2\)
so, to shift it
\(\bf f(x) = x^2\\\quad \\
\textit{shifted to the left by }8 \qquad \implies (x+8)^2\\\quad \\
\textit{pelleted up by }2 \qquad \implies (x+8)^2+2\)

Answer 8

pelleted? heheh,

Answer 9

lol I have a typo.... hhehe

Answer 10

\(\bf f(x) = x^2\\\quad \\
\textit{shifted to the left by }8 \qquad \implies (x+8)^2\\\quad \\
\textit{shifted up by }2 \qquad \qquad \implies (x+8)^2+2\\\quad \\
g(x) = (x+8)^2+2\)

Answer 11

Ooh lol thank you