Question

Which functions graph is a translation of the graph of f(x)= 3x^2 + 4 seven units down?

A. F(x)= -4x^2 +4
B. F(x)= 10x^2+4
C. F(x)= 3x^2-3
D. F(x)= 3x^2 +11

Answer 1

Option C

Explanation:

Consider the function f ( x ) = 3x^2 + 4;

`f ( x ) = 3x^2 + 4,\\\\4 = vertex ( y - intercept ),\\\\\\`

Now if this graph were to be translated 7 units down, considering the function was f ( x ) = 3x^2, the new graph would be f ( x ) = 3x^2 - 7. The same concept is applied to the graph f ( x ) = 3x^2 + 4;

`4 - 7 = - 3,\\f ( x ) = 3x^2 - 3\\\\Solution - Option C`

* Note that a translation doesn't effect the rate with which the graph changes, it only effect's it's position on the coordinate plane

Hope that helps!