which translation maps the graph of the function $f(x)=x^{2}$ onto the function $g(x)=x^{2}+2x + 6$?\nleft 1…

Explanation:

Step1: Rewrite $g(x)$ in vertex - form

Complete the square for $g(x)=x^{2}+2x + 6$. We know that $x^{2}+2x+6=(x^{2}+2x + 1)-1 + 6=(x + 1)^{2}+5$.

Step2: Recall the rules of function translation

For a quadratic function $y = f(x)=x^{2}$, and $y = g(x)=(x - h)^{2}+k$, the graph of $y = f(x)$ is translated $h$ units horizontally and $k$ units vertically. Here $h=-1$ and $k = 5$. A negative $h$ value means a left - hand translation and a positive $k$ value means an upward translation. So the graph of $f(x)=x^{2}$ is translated 1 unit to the left and 5 units up to get the graph of $g(x)=(x + 1)^{2}+5$.

Answer:

left 1 unit, up 5 units