Question

Given f(x)=x2, after performing the following transformations: shift upward 58 units and shift 75 units to the right, the new function g(x)=

Performing transformations

Given $$f(x)=x2$$, after performing the following transformations: shift upward 58 units and shift 75 units to the right, the new function $$g(x)=$$

2021-02-06

Given $$f(x)=x^2$$
Transformations
upward shift$$=58$$ units
right shift$$=75$$ units
when f(x) is shift upwards 58 then $$g(x)=f(x)+58$$
when f(x) is shifted right by 75 units
$$g(x)=f(x-75)+58$$
when f(x) is shifted upwards 58 units then
$$g(x)=f(x)+58$$
when f(x) is shift right by 75 units
$$g(x)=f(x-75)+58$$
$$g(x)=(x-75)^2+58$$
In simplified form
$$g(x)=x^2-150x+5625+58$$
$$g(x)=x^2-150x+5683$$