Question

The quadratic functions f(x) and g(x) are described as follows:

Answer 1

Given:

f(x) and g(x) are two quadratic functions.

$f(x)=-8x^2-7$

The table of values for the function g(x) is given.

To find:

The statement that best compares the maximum value of the two functions.

Solution:

We have,

$f(x)=-8x^2-7$

Here, the leading coefficient is -8 which is a negative number. So, the function f(x) represents a downward parabola.

We know that the vertex of a downward parabola is the point of maxima.

The vertex of a quadratic function $f(x)=ax^2+bx+c$ is:

$Vertex=\left(\dfrac{-b}{2a},f(-\dfrac{b}{2a})\right)$

In the given function, $a=-8,b=0,c=-7$.

$-\dfrac{b}{2a}=-\dfrac{0}{2(-8)}$

$-\dfrac{b}{2a}=0$

Putting $x=0$ in the given function, we get

$f(0)=-8(0)^2-7$

$f(0)=-7$

So, the vertex of the function f(x) is at (0,-7). It means the maximum value of the function f(x) is -7.

From the table of g(x) it is clear that the maximum value of the function g(x) is 6.

Since $6>-7$, therefore g(x) has a greater maximum value than f(x).

Hence, the correct option is C.

Answer 2

Answer: the other answer is wrong the right one is

f(x) has a greater maximum value than g(x).

Step-by-step explanation: