Question

If the graph of the function f defined by

f(x)=3x^2-5
is translated vertically upward by 8 units, it becomes the graph of a function g.
Find the expression for g(x)

Answer 1

g(x) = 3x^2 + 3.

Explanation:

f(x) = 3x^2 - 5.

First, the x-intercepts have to be calculated to determine the line of symmetry of f(x). For that, set f(x) = 0. Therefore:

3x^2 - 5 = 0.

x^2 = 5/3

x = 1.29 and x = -1.29. The midpoint of these two x-coordinates will be the line of symmetry, which is x = 0.

Therefore, if the graph is translated vertically upwards, it will move up the y-axis by the given amount. In this question, the amount is 8. Simply add 8 in f(x) to obtain g(x). Therefore:

g(x) = f(x) + 8.

g(x) = 3x^2 - 5 + 8.

g(x) = 3x^2 + 3.

Therefore, g(x) = 3x^2 + 3!!!