Question

The function g(x) is a translation of f(x) = (x + 3)2 – 10. The axis of symmetry of g(x) is 5 units to the right of f(x) . Which function could be g(x)?

Answer 1

Answer:

There are two possible solutions for $g(x)$:

$g(x) = (x+3)^{2}-5$

$g(x) = x^{2}-3\cdot x +4$

Step-by-step explanation:

From statement, we understand that $g(x)$ is defined by the following operation:

$g(x) = f(x) +5$ (1)

If we know that $f(x) = (x+3)^{2}-10$, then $g(x)$ is defined by:

$g(x) = (x+3)^{2}-10+5$

$g(x) = (x+3)^{2}-5$

$g(x) = x^{2}-3\cdot x + 9 -5$

$g(x) = x^{2}-3\cdot x +4$