Answer:
The option which is:
On a coordinate plane, a parabola opens up. It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10).
Step-by-step explanation:
At first we should know the rules of translation
1) {f(x) + a} is f(x) shifted up (a) units
2) {f(x) – a} is f(x) shifted down (a) units
3) {f(x + a)} is f(x) shifted left (a) units.
4) {f(x – a)} is f(x) shifted right (a) units.
Given:
f(x) = x²
g(x) = (x-5)² + 1
By comparing [ the translation from f(x) to g(x) ] with the rules of translation
We can deduce that g(x) is the image of f(x) by translation 5 units right and 1 unit up ( rules 1 and 4)
See the attached figure which represent the graph of f(x) and g(x)
As shown g(x) goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10)
