Question

Find g(x), where g(x) is the translation 7 units up of f(x)=x2.

Write your answer in the form m(x+a)2+b, where m, a, and b are integers.

g(x)=?

Answer 1

The process of transformation under translation means that the figure is simply change into another position. That is, the angles, the lengths or any other characteristic is unchanged except for the position of the figure in the Cartesian coordinate alone.
We are given the function in the form of:

f(x) = x^2

Which can also be written as:

y = x^2

Since the translation made is to move the figure 7 units up, then this means that the y coordinate is increased by 7. The given equation is a parabola pointing up with vertex at (0, 0). So moving it up would move the vertex at point (0, 7). The vertex of y is represented by the variable b, therefore b = 7 which further gives us the function:

y' = x^2 + 7

or

g(x) = x^2 + 7