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

Answer 1

The quadratic parent function is given by $f(x)=x^2$. When we apply transformations to create $g(x)=f(x-3)+5$, we can analyze the transformations as follows:

1. Horizontal Shift: The term $(x-3)$ 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 $f(x)=x^2$ 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 $(3,5)$.