Question

how do i identify the horizontal translation of the parent function, f(x)= x squared
y=(x-4) squared

Answer 1

\[f(x)=a(x-h)^{2}+k\]
the horizontal shift is the value of x that makes (x-h) = 0

Answer 2

for yours, you have

\[f(x)=(x-4)^{2}\]
what value of x makes (x-4) = 0?

Answer 3

so basically plug in f(x) for y?

Answer 4

?

Answer 5

if
\[f(x) = x^{2}\] is the parent function and
\[g(x)=(x-4)^{2}\] is the transformed function then g(x) is a horizontal shift of f(x).

The amount of horzontal shift is given by finding what value of x makes the (x-4) term equal 0.