Question

The quadratic function f(x) has a vertex at (9, 8) and opens upward. If g(x) = 4(x − 8)2 + 9, which statement is true?
A.
The maximum value of f(x) is greater than the maximum value of g(x).
B.
The maximum value of g(x) is greater than the maximum value of f(x).
C.
The minimum value of f(x) is greater than the minimum value of g(x).
D.
The minimum value of g(x) is greater than the minimum value of f(x).

Answer 1

ANSWER

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

EXPLANATION

It was given that;

$f(x)$
has a vertex at

$(9,8)$

and opens upwards.

This means that f(x) is a minimum graph and hence have a minimum value of 8.

Also ,

$g(x) = 4 {(x - 8)}^{2} + 9$

When we compare this function to

$y = a {(x - h)}^{2} + k$

We can see that,a=4, h=8 and y=9.

The vertex is

$(8,9)$

Since a>0, the graph opens upwards.

The graph has a minimum point which is (8,9) and hence the minimum value is 9.

We can see that, the minimum value of g(x) is greater than the minimum value of f(x).

Therefore the correct answer is D.