For this case , the parent function is given by [tex f (x) =x^2 [\tex] We apply the following transformations Vertical translations : Suppose that k > 0 To graph y=f(x)+k, move the graph of k units upwards For k=9 We have [tex]h(x)=x^2+9 [\tex] Horizontal translation Suppose that h>0 To graph y=f(x-h) , move the graph of h units to the right For h=4 we have : [tex ] g (x) =(x-4) ^ 2+9 [\tex] Answer : The function g(x) is given by G(x) =(x-4)2 +9
If it’s horizontally translated, the x value/ input is altered, meaning that the value is added or subtracted from x. In this case, you move 4 units to the right, so you’d have (x-4)^2. Then vertical change is shown by changes to the y value, so it would be outside the parentheses. So you get +9 out of the parentheses.
