Question

the graph of f(x), shown below, resembles the graph of g(x) = x2, but it has been changed somewhat. which of the following could be the equation of f(x)?

Answer 1

Just try numbers! D is correct

Answer 2

Answer: $f(x)=0.4x^2-1$

Explanation: given function is $g(x)= x^2$

Since, According to the given statement we get f(x)  by doing some changes in g(x).

And, After seeing the given figure, we can say that the end behavior of f(x) is same as g(x). So, function f(x) must has even degree with positive leading coefficient.

Now, again according to the graph it seems f(x) is obtained by shifting g(x),  1 unit vertically downward.

And, also it is compressed by some unit less than 1.

So it is the type of $f(x)=ax^2-1$ where a is  must be a positive number less than 1.  ( because here vertical compression occurs)

Since, from the given options , only Option D is showing the above conditions.

Therefore Option D. $f(x)=0.4x^2-1$ is the correct function for the given graph.