Determine the equation of g(x) that results from translating the function f(x) = x2 + 7 upward 9 units.

Question

Determine the equation of g(x) that results from translating the function f(x) = x2 + 7 upward 9 units.

Answer 1

To translate up (or down) add (or subtract) from the value of the function.

 

f(x) = x² + 7 + 9    moves the graph up 9 units

 

f(x) = x² + 16

Answer 2

You are trying to ranslating the function f(x) = x^2 + 7 upward 9 units. 

ie. if (h, k) is a point on f(x), (h, k+9) is a point on g(x).

 

k+9 = g(h)  as (h, k+9) is on g(x), by the same logic,  k=f(h)

 

or g(h)=  k + 9 = f(h) + 9 = h^2 + 7 + 9 = h^2 + 16

 

Replacing h with x, we have g(x) = x^2 + 16.