Answer:
Correct answer is:
C. [tex]F(x) =-x^{2} -3[/tex]
Step-by-step explanation:
We are given a function:
[tex]G(x) = x^{2}[/tex]
The graph of [tex]G(x)[/tex] is also shown in the given question figure.
It is a parabola with vertex at (0,0).
Sign of [tex]x^{2}[/tex] is positive, that is why the parabola opens up.
General equation of parabola is given as:
[tex]y = a(x-h)^2+k[/tex]
Here, in G(x), a = 1
Vertex (h,k) is (0,0).
As seen from the question figure,
The graph of F(x) opens down that is why it will have:
Sign of [tex]x^{2}[/tex] as negative. i.e. [tex]a = -1[/tex]
And vertex is at (0,-3)
Putting the values of a and vertex coordinates,
Hence, the equation of parabola will become:
[tex]y = -1(x-0)^2+(-3)\\y = -x^2-3[/tex]
The correct answer is:
C. [tex]F(x) =-x^{2} -3[/tex]
The required equation of graph f(x) is [tex]y = -x^{2} -3[/tex]
Given that,
The graph of f(x), resembles the graph of G(x) = [tex]x^{2}[/tex].
We have to find,
Which of the following could be the equation of f(x).
According to the question,
Function, [tex]G(x) = x^{2}[/tex],
The graph in the given question figure. It is a parabola with vertex at (0,0).
By the graph predict that Sign of [tex]x^{2}[/tex] is positive, that is why the parabola opens up.
General equation of parabola is given by,
[tex]y = a(x-h)^{2} +k[/tex]
Where, a = 1, and vertex (h, k) is (0,0).
The graph of F(x) unknown function opens down ,
Sign of [tex]x^{2}[/tex] as negative. and the vertex is at (0,-3)
To find the equation of function f(x),
Putting the values of a and vertex coordinates,
[tex]y = a(x-h)^{2} +k[/tex]
The equation of parabola become:
[tex]y = -1(x-0)^{2} +(-3)\\\\y = -x^{2} -3[/tex]
Hence, The required equation of f(x) is [tex]y = -x^{2} -3[/tex].
For more information about Parabola click the link given below.
https://brainly.com/question/4074088
