Question

a quadratic function $y = f(x)$ is plotted on a graph and the vertex of the resulting parabola is $(6, -3)$. what is the vertex of the function defined as $g(x) = f(x + 3) + 5$?

Explanation:

Step1: Handle horizontal shift

For $f(x+3)$, replace $x$ with $x+3$ in the vertex $x$-coordinate: $6 - 3 = 3$

Step2: Handle vertical shift

Add 5 to the vertex $y$-coordinate: $-3 + 5 = 2$

Answer:

$(3, 2)$