Question

question a quadratic function y = f(x) is plotted on a graph and the vertex of the resulting parabola is (-6, -4). what is the vertex of the function defined as g(x)=f(x)+2? answer attempt 1 out of 2

Explanation:

Step1: Recall vertical - shift rule

For a function $y = f(x)$ and $y = f(x)+k$, the graph of $y = f(x)+k$ is a vertical shift of the graph of $y = f(x)$ by $k$ units. If $k>0$, the shift is upward; if $k < 0$, the shift is downward.

Step2: Analyze the given functions

We have $g(x)=f(x) + 2$. This means the graph of $g(x)$ is the graph of $f(x)$ shifted upward by 2 units. The vertex of $f(x)$ is shifted upward by 2 units to get the vertex of $g(x)$. Given the vertex of the graph of $y = f(x)$ (the original quadratic function) after some transformation to get $g(x)$ has a vertex of $(-6,-4)$.

Step3: Calculate the new vertex

Let the vertex of $f(x)$ be $(h,k)$. The vertex of $g(x)=f(x)+2$ is $(h,k + 2)$. Substituting $h=-6$ and $k=-4$ into $(h,k + 2)$, we get $(-6,-4 + 2)$.
$(-6,-2)$

Answer:

$(-6,-2)$