Answer:
\(5\) units to the right and \(23\) units down
Step-by-step explanation:
we have
\(f(x)=x^{2}\)
This is a vertical parabola open upward with vertex at point \((0,0)\)
\(g(x)=x^{2} -10x+2\)
Step 1
Convert the function g(x) into vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
\(g(x)-2=x^{2} -10x\)
Complete the square. Remember to balance the equation by adding the same constants to each side
\(g(x)-2+25=x^{2} -10x+25\)
\(g(x)+23=x^{2} -10x+25\)
Rewrite as perfect squares
\(g(x)+23=(x-5)^{2}\)
\(g(x)=(x-5)^{2}-23\)
The function g(x) is a vertical parabola with the vertex at point \((5,-23)\)
Step 2
Find the rule of the translation
\((0,0)-------> (5,-23)\)
\((x,y)-------> (x+5,y-23)\)
That means
The translation is \(5\) units to the right and \(23\) units down
