the graphs of y = f(x) and y = g(x) appear below. if g(x) = f(x + c), what is the value of c?

Explanation:

Step1: Identify vertex - shift rule

The graph of $y = f(x + c)$ is a horizontal shift of the graph of $y=f(x)$. If $c>0$, the graph shifts left; if $c < 0$, the graph shifts right.

Step2: Locate vertex of $f(x)$ and $g(x)$

The vertex of $y = f(x)$ is at $x = 0$ (the maximum point of the parabola), and the vertex of $y = g(x)$ is at $x=3$.

Step3: Calculate the value of $c$

We know that $g(x)=f(x + c)$. To get from the $x$-coordinate of the vertex of $f(x)$ to the $x$-coordinate of the vertex of $g(x)$, we use the transformation. If we start with $x = 0$ for $f(x)$ and end up with $x = 3$ for $g(x)$, we have $0 + c=3$, so $c = 3$.

Answer:

$3$