Respuesta :
Given:
f(x) and g(x) are two quadratic functions.
[tex]f(x)=-8x^2-7[/tex]
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,
[tex]f(x)=-8x^2-7[/tex]
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 [tex]f(x)=ax^2+bx+c[/tex] is:
[tex]Vertex=\left(\dfrac{-b}{2a},f(-\dfrac{b}{2a})\right)[/tex]
In the given function, [tex]a=-8,b=0,c=-7[/tex].
[tex]-\dfrac{b}{2a}=-\dfrac{0}{2(-8)}[/tex]
[tex]-\dfrac{b}{2a}=0[/tex]
Putting [tex]x=0[/tex] in the given function, we get
[tex]f(0)=-8(0)^2-7[/tex]
[tex]f(0)=-7[/tex]
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 [tex]6>-7[/tex], therefore g(x) has a greater maximum value than f(x).
Hence, the correct option is C.
Answer: the other answer is wrong the right one is
f(x) has a greater maximum value than g(x).
Step-by-step explanation:
