The function rule for g(x) is g(x) = (x - 5)^2 + 10 or simply g(x) = 10. This is because the graph shows a parabola shifted 5 units to the right and 10 units up, with a vertex at (5, 10).
The function rule for g(x) is:
g(x) = (x - 5)^2 + 10
Identify the vertex of the parabola. The vertex of the parabola in the graph is (5, 10).
Since g(x) is a translation of f(x) = x², it can be written in the form:
g(x) = a(x + h)² + k
where (h, k) is the vertex of the parabola.
Substitute the vertex of the parabola into the equation to get:
g(x) = a(x - 5)² + 10
We can also see from the graph that the parabola passes through the point (9, 10). We can plug this point into the equation to solve for a:
10 = a(9 - 5)² + 10
10 = 16a + 10
16a = 0
a = 0
Therefore, the function rule for g(x) is:
g(x) = 0(x - 5)² + 10
or simply:
g(x) = 10
This is because any function of the form a(x - h)² + k, where a = 0, is simply a horizontal line at the height k.