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Please look at the screen shot below it is about Linear Functions

Please look at the screen shot below it is about Linear Functions-example-1
User JoJoS
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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.

User Tkbx
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