Question

State the various transformations applied to the base function f(x) =x^ 2 to obtain a graph of the tlong (x) = (x - 3) ^ 2 + 5

Answer 1

Answer:

The base function was shifted 3 units right and 5 units up to obtain the transformed function.

Step-by-step explanation:

The base function is

$f(x) = {x}^{2}$

This is a parabola that opens up with vertex at origin.

The transformed parabola has equation:

$g(x) = {(x - 3)}^{2} + 5$

Comparing to

$g(x) = a {(x - h)}^{2} + k$

We have the vertex of the transformed function at (h,k)=(3,5).

This is in the first quadrant.

This means the base function was shifted 3 units right and 5 units up.