Question

Consider the functions f(x) and g(x):

f(x) = (x - 5)^2 - 10
g(x) = (x + 10)^2

Which function has its vertex at (5, -10)?
A. f(x)
B. g(x)
C. Both functions have the same vertex.
D. None of the above

Answer 1

Function f(x) has its vertex at (5, -10) because it is in vertex form with h=5 and k=-10. Function g(x) has a different vertex, therefore, the answer is A. f(x).

Step-by-step explanation:

To determine which function has its vertex at (5, -10), we need to analyze the given functions f(x) = (x - 5)2 - 10 and g(x) = (x + 10)2. The vertex form of a quadratic function is given by f(x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola. In the case of the function f(x), we can identify the values of h and k directly from the equation. Here, h=5 and k=-10 which means the vertex for f(x) is at (5, -10).

In contrast, for function g(x), the vertex can be found using the same method. However, in this case, h=-10 and k=0, which does not match the given vertex (5, -10). Therefore, the correct answer is A. f(x).