Question

question: a quadratic function y = f(x) is plotted on a graph and the vertex of the resulting parabola is (-6,6). what is the vertex of the function defined as g(x)=f(x)-3? answer: empty input box

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 $y = f(x)$ down by $k$ units. If the vertex of $y = f(x)$ is $(h, v)$ and $y = g(x)=f(x)-3$, the $x$ - coordinate of the vertex remains the same and the $y$ - coordinate of the vertex changes.

Step2: Calculate the vertex of $f(x)$

Let the vertex of $f(x)$ be $(h, v)$ and the vertex of $g(x)=f(x) - 3$ be $(h, v - 3)$. We know that the vertex of $g(x)$ is $(-6,6)$. So, if $h=-6$ and $v-3 = 6$, then we can solve for $v$.

Step3: Solve for $v$

Add 3 to both sides of the equation $v - 3=6$. We get $v=6 + 3=9$. So the vertex of $f(x)$ is $(-6,9)$.

Answer:

$(-6,9)$