the quadratic parent function f was transformed to create g(x) = f(x - 3) + 5. what is the vertex of the graph of g

1 answer

The quadratic parent function is given by f(x)=x2. When we apply transformations to create g(x)=f(x3)+5, we can analyze the transformations as follows:

  1. Horizontal Shift: The term (x3) indicates a horizontal shift to the right by 3 units. This moves the vertex from its original position.

  2. Vertical Shift: The term +5 indicates a vertical shift upwards by 5 units.

The vertex of the parent function f(x)=x2 is at the point (0,0).

Applying the transformations:

  • After shifting right by 3 units, the new x-coordinate of the vertex becomes 0+3=3.
  • After shifting up by 5 units, the new y-coordinate of the vertex becomes 0+5=5.

Thus, the vertex of the graph of g(x) is at the point (3,5).