Question

Which pair of functions has the vertex of k(x)k(x) positioned 5 units below the vertex of f(x)f(x)?

A. f(x)=x² and k(x)=(x+5)²
B. f(x)=x² and k(x)=x2−5
C. f(x)=x²and k(x)=x2+5
D. f(x)=x² and k(x)=(x−5)²

Answer 1

The correct pair of functions that has the vertex of k(x) positioned 5 units below the vertex of f(x) is Option D: f(x)=x² and k(x)=(x-5)².

Step-by-step explanation:

The correct pair of functions that has the vertex of k(x) positioned 5 units below the vertex of f(x) is Option D: f(x)=x² and k(x)=(x-5)².

To determine the position of the vertices, we use the formula x = -b/(2a) for a quadratic function in the form of f(x) = ax² + bx + c. In this case, the x-coordinate of the vertex of f(x) is 0, and the x-coordinate of the vertex of k(x) is 5.

Therefore, the vertex of k(x) is 5 units below the vertex of f(x).