Question

1. if $f(x) = x^2$ and $g(x) = f(x + 7.2)$, what is the vertex of the graph of $g$?

options:
(7.2, 0)
(-7.2, 0)
(0, 7.2)
(0, -7.2)

Explanation:

Step1: Identify vertex of $f(x)$

The function $f(x)=x^2$ is a standard parabola, its vertex is $(0,0)$.

Step2: Analyze horizontal shift for $g(x)$

$g(x)=f(x+7.2)$ means a left shift by 7.2 units.
For a horizontal shift $f(x-h)$, here $h=-7.2$, so subtract 7.2 from the x-coordinate of $f(x)$'s vertex.
New x-coordinate: $0 - 7.2 = -7.2$, y-coordinate stays 0.

Answer:

$(-7.2, 0)$