Question

what is the function ( g(x) ) created from ( f(x) = x^2 ) by moving the graph right 8 units, vertically stretching it by a factor of 3, and shifting the graph up 6 units?
a ( g(x) = 8(x + 3)^2 + 6 )
b ( g(x) = 3(x - 8)^2 + 6 )
c ( g(x) = 3(x + 8)^2 + 6 )
d ( g(x) = 8(x + 3)^2 + 6 )

Explanation:

Step1: Apply horizontal right shift

For a right shift of 8 units, replace $x$ with $x-8$ in $f(x)$:
$f_1(x) = (x-8)^2$

Step2: Apply vertical stretch by 3

Multiply the function by 3:
$f_2(x) = 3(x-8)^2$

Step3: Apply vertical upward shift

Add 6 to the function:
$g(x) = 3(x-8)^2 + 6$

Answer:

B. $g(x)=3(x-8)^2 + 6$