Question

The quadratic function f has a vertex at (3,4) and opens upward. The quadratic function g is shown below. Which statement is true? A. The minimum value of g is greater than the minimum value of f. B. The maximum value of g is greater than the maximum value of f. C. The minimum value of f is greater than the minimum value of g. D. The maximum value of f is greater than the maximum value of g.

Answer 1

The minimum value of f(x) is greater than the minimum value of g(x).

Explanation:

Given

`(h_1,k_1) = (3,4)` --- vertex of f(x)

`g(x) = 4(x - 4)^2 + 3` --- g(x) equation

Required

Which of the options is true

First, we identify the vertex of g(x)

A quadratic function is represented as:

`g(x) =a(x - h)^2 + k`

Where:

`(h,k) \to` vertex

So, we have:

`(h_2,k_2) = (4,3)`

`a = 4`

If
`a>0`, then the curve opens upward

From the question, we understand that f(x) also open upward. This means that both functions have a minimum

The minimum is the y (or k) coordinate

So, we have:

`(h_1,k_1) = (3,4)` --- vertex of f(x)

`(h_2,k_2) = (4,3)` --- vertex of g(x)

The minimum of both are:

`Minimum = 4` ---- f(x)

`Minimum = 3` ---- g(x)

By comparison:

`4 > 3`

Hence, f(x) has a greater minimum

Answer 2

The minimum value of f(x) is greater than the minimum value of g(x).

Explanation: