Question

The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1. On a coordinate plane, a parabola, labeled f of x, opens up. It goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). Which graph represents g(x)? On a coordinate plane, a parabola opens up. It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10). On a coordinate plane, a parabola opens up. It goes through (2, 8), has a vertex at (5, negative 11), and goes through (8, 8). On a coordinate plane, a parabola opens up. It goes through (negative 8, 10), has a vertex at (negative 5, 1), and goes through (negative 2, 10). On a coordinate plane, a parabola opens up. It goes through (negative 8, 8), has a vertex at (negative 5, negative 11), and goes through (negative 2, 8).

Answer 1

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).

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)