The quadratic function f has a vertex at (3,4) and opens upward. The quadratic function g is shown below. Which statement is true?

Answer and Step-by-step explanation:

In the complete question, the function g is given as 2(x-4)² + 3 and the statements are:

The minimum value of g is greater than the minimum value of f.

The minimum value of f is greater than the minimum value of g.

The maximum value of f is greater than the maximum value of g.

The maximum value of g is greater than the maximum value of f.

Since f has a vertex at (3,4) and it opens upwards, then it has a minimum at 4.

The given function is

2(x-4)² + 3

The standard vertex equation is:

a(x–h)² + k where (h,k) is the vertex and a is a constant.

Comparing that to the given equation we see that:

(h,k) = (4,3) and a = 2

The parabola opens upwards as well since a=2 (positive), therefore it has a minimum of 3.

From here we see that the minimum of f is 4 and minimum of g is 3. Therefore, the minimum value of f is greater than the minimum of value g.