Question

Find g(x), where g(x) is the translation 3 units down of f(x)=x^2

Answer 1

Answer:

g(x)=x² -3

Step-by-step explanation:

Vertical and horizontal translations are the displacements of a function in the coordinate system (x, y). By transferring the graphical representation of a given function, we obtain representations of related functions. The graph of the translated function will always be the same as the original.

When performing a vertical translation of a function, the graph will move from one point to another determined point in the direction of the "y" axis, that is, up or down.

So, the algebraic expression of the parabola that results from moving the parabola f (x) = x² vertically is f (x) = x² + q

• If q> 0, the parabola moves q units up.

• If q <0, the parabola moves q units down.

So the vertex of the parabola is at the point (0, q).

So if the function f (x) = x² is translated 3 units down, the function g (x) will be:

g(x)=x² -3